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HINRICHS' 

ELEMENTS OF PHYSICS. 



Con sensate esperienze confirmano i principij che sono 
i fondamenti di tutte la seguente struttura. 
Galileo Galilei. 



THE RLE ENTS 



OF 



PHYSICAL SCIENCE, 

DEMONSTRATED BY 

THE STUDENT'S OWN EXPERIMENTS 
AND OBSERVATIONS. 

BY 

GUSTAVUS HINRICHS, A. M. 



IN THREE VOLUMES. 



VOLUME I. 

THE ELEMENTS OF PHYSICS. 

WITH A PLATE. 



DAVENPORT. IOWA, U. S. 

PUBLISH!:!) BY GRIGGS, WATSON, & OAY, 

LEIPZIG: V. A. BBOCKHAU8. 

1870. 



1 3 



THE 



, ELEMENTS OF PHYSICS, 



DEMONSTRATED BY 



; 



THE STUDENT'S OWN EXPERIMENTS. 



BY 



6USTAVUS H1NRICHS, A. M. 

Professor of Physical Science in the State University of Iowa; Member, or 

Correspondent, of Scientific Societies at Berlin, Vienna. 

Koenigsberg, Emden, etc. etc. 



WITH A PLATE. 



DAVENPORT, IOWA, U. S. 
PUBLISHED BY GRIGGS, WATSON & DAY, 

LEIPZIG : F. A. BROCKHAUS, 

1870. 



*V 



Entered according to act of Congress, in the year 1870, by 

GUSTAYUS HINRICHS, 
In the office of the Librarian of Congress, at Washington. 



I lie right of translation and republication reserved 
by the author. 



/ ST/? 



9/ 

PKEFACE. 



It is generally admitted by those qualified to judge, that the teach- 
ing of elementary science in our schools is not carried on in a scien- 
tific spirit. Recitation from a text book, with occasional exhibition 
of experiments and specimens, is not calculated to give the beginner 
conviction in the truth stated, or to initiate him into the method of 
scientific investigation. 

In regard to science, our schools are not above the middle ages. 
Three hundred years ago students repeated the obscure statements of 
Aristotle, of which a sample is given (454); now our students repeat 
the statements of their text book, without obtaining any valid ground 
for the conviction they are made to express. 

The great work done by Galileo for physical science in general, 
has not yet reached our schools. The method of scientific research, 
which he first so successfully practiced, and which alone can lead to 
conviction in the truth of the results obtained, has not yet gained admis- 
sion to our schools. 

We venture with the present little work to knock at the doors of 
our schools in behalf of this method and in the interest of science. 
We do not advocate anything new. For two and a half centuries 
these very methods have been used, the grand structure of modern sci- 
ence has resulted, and the course of civilization has been changed 
thereby. 

That these same methods are successful in the school room and with 
beginners, is not a mere conclusion, but a fact established by experi- 
ence. The few series of experiments printed in the " Journal" of 
this 'volume, will confirm it. The series here published have been 
taken from an immense material already accumulated by students in 
our laboratory. 

But this work is so thoroughly different from those which are in 
general use, that we feel under great obligations to the Publishers for 
having ventured this publication. 

Before attempting the use of this book, the student, and especially 
the teacher, should carefully study the Guide at the close of this volume. 



CONTENTS. 



CHAPTER I.— Magnitude and Weight. 




I. Length . . . . . 


1 


II. Volume ...... 


4 


III. Weight . . . 


6 


IV. Specific Gravity ..... 


. 10 


Appendix (Angles and Time) 


. 13 


V. Mensuration ..... 


. 15 


VI. Linear Drawing ..... 


. 25 


CHAPTER II. — Mechanical Work, and Machines 


. 42 


CHAPTER III.— Molecular Properties of Matter. 




I. States of Aggregation .... 


. 59 


II. Molecular Properties of Liquids 


. 62 


III. Molecular Properties of Gases 


. 71 


IV. Molecular Properties of Solids . 


. 79 


V. Solution and Crystallization 


. 82 


VI. Crystallography ..... 


. 88 


CHAPTER IV.— On Light and Vision. 




I. Lustre and Color .... 


. 102 


II. The Prism and the Spectrum 


. 105 


III. The Lens, and Optical Images 


. 109 


IV. The Telescope 


. 114 


V. The Microscope . . 


. 120 


VI. Appendix ...... 


. 122 


CHAPTER V. — Electricity and Magnetism. 




I. Magnets ...... 


. 125 


H. The Earth-Magnet .... 


. 130 


HI. Friction Electricity .... 


. 132 


IV. Galvanism ..... 


. 138 


V. Electro-Magnetism .... 


. 143 


VI. Induction ...... 


. 148 


VH. Conclusion ..... 


. 151 


Guide to the Study of the Elements of Physics 


. 153 


Problems and Reduction .... 


. 164 


Journal of Experiments ..... 


. 169 



CHAPTER I. 



MAGNITUDE AND WEIGHT. 



All bodies possess magnitude ; that is, extension in 
space. The words bulk and size are, at times, used instead 
of the term magnitude. 

Length (Z), breadth (5), and height (A), measure the ex- 
tension of bodies in three different directions, usually at 
right angles to one another. 

2. The extensions in these three directions at right 
angles to each other are also called the dimensions of a 
body. 

The third dimension, A, is called height when reckoned 
upwards^ depth when reckoned dowmvards, and thickness 
when mere extension is referred to. 

I. LENGTH. 

3. The unit of length is the meter. The standard meter, 
adopted by an international committee, is preserved in the 
archives in Paris, and copies thereof are to be found in 
the archives of all civilized nations. The meter is very 
nearly the ten-millionth part of the arc on the earth's sur- 
face passing through Paris, due north and south frcm the 
pole to the equator. 

4. This meter is the basis of the metric system of weights 
and measures, wherein the units are continually multiplied 
or divided by ten. 

In this system all measures and weights are, therefore^ 
decimal — exactly like the numbers we use. See exam- 
ples in the subsequent (6). Hence, all calculations can be 
performed as with common numbers. 

In older systems of measures and weights, the divisions 
were all at variance with the numbers we use for calcula- 
tion ; hence much time was lost in reducing a measure or 
weight from one unit to another. 
1 



Chapter I. 



These older systems are obsolete in science, and disap- 
pear more and more from common life. Many of the 
great nations of the continent have adopted the metric sys- 
tem, and made its use compulsory. England and the 
United States have legalized the use of the same. In 
science it has, as above stated, long been very generally 
used. 

5. The multiples of the unit are always denoted by a 
prefix, derived from the Greek name of the corresponding 
number. The following are the prefixes used : — 

PREFIX. 

10 deca. 

100 hecto. 

1,000 kilo. 

10,000 myria. 

The divisions, or sub-multiples, are denominated by a 
prefix expressing the Latin name of the number which is 
divided into the unit: — 

PREFIX. 

Vio deci. 

Vioo • centi. 

Viooo milli. 

6. The names of the multiples and divisions of the unit 
meter are according^ : — 

Unit 1 meter. 



DIVISIONS. 

x /io meter. ..1 deci-meter. 

Vioo u . ..1 centi-meter. 

Viooo " . ..1 milli-meter. 



MULTIPLES. 

10 meters, 1 deca-meter. 
100 " 1 hecto-meter. 
1,000 " 1 kilo-meter. 
10,000 " 1 myria-meter 

The abbreviations most commonly used are, m. for me- 
ter, and mm. for millimeter; also cm. for centimeter. 
Pot example: 52 m. is the same as 5,200 em. or 52,000 m 
m. ; and 79,813 mm. is 79 m. (or 7 decameters, 9 meters), 
8 decimeters, 1 centimeter, and 3 millimeters. 

This example also shows how easy it is to reduce one 
unit to another in this system. 

7. The most convenient measure for the students is a 
centimeter scale, 10 cm. or one decimeter long. In or- 
der to obtain the tenths or millimeters, an additional 



Length. 3 

centimeter, divided into millimeters, has been drawn 
beyond the zero. The student should copy this scale on a 
strip of white card paper, about 12 cm. long and 1 cm. 
wide. Use this scale for measuring smaller dimensions. 
Also make a meter rule, divided into decimeters, with the 
last decimeter divided into centimeters. Use this rule 
for measuring greater dimensions. When a scale several 
meters long is to be used, divide the same into decimeters, 
and use a card millimeter scale, one decimeter long, for 
the determination of the ma (See plate 1, fig. 1.) 

If no standard is at hand, carefully mark the diameter 
of a nickel five-cent piece on paper, for this diameter is, 
according to law, 20 mm. It is near enough So for the 
beginner. 

8. Practice. — The student should now carefully measure 
the dimensions of at least ten different objects near him, 
and neatly record these measurements in his journal (blank 
book). Such smaller objects to be measured by the centi- 
meter scale are : The inch English measure ; the length 
and diameter of a lead pencil ; a glass rod, glass tubes, etc. 
Also estimate by sight the dimensions of such small bodies, 
and also of pins, nails, etc. ; and thereafter measure the 
same, entering name, estimated and measured dimensions, 
in your note-book. 

With the meter rule you can measure tables, cases, etc., 
in the school room ; also the dimensions of the tables. It 
is best to draw a sketch of all objects measured, and either 
to enter the measures found upon this sketch, or to letter 
the sketch and tabulate the measures on another part of 
the paper. (See plate 1, fig. 2.) 

By means of a tape divided into decimeters, distances 
in the field and garden may be measured for practice, 
xllways carefully enter the result in your note book. 



Chapter I. 



II. VOLUME. 

9. The unit of volume most used in physical science is 
the cub nneter, and denoted cc. It is a cube, each 

6dge of which is one centimeter in length. 

The unit of volume used in commerce is the litre, equal 
to one thousand cubic centimeters. Hence the cubic centi- 
meter is Yiooo of a litre, or a millilitre. The following 
table shows the above prefixes in actual use : — 

Unit 1 litre. 



SUB-MULTIPLES. 

l /io litre 1 deci-litre. 

1 / 100 " 1 centi-litre. 

Viooo " ; 1 milli-litre. 



MULTIPLES. 

10 litres. ..1 deca-litre. 
100 " . . . 1 hecto-litre. 
1,000 " ...1 kilo-litre. 
10,000 " ...1 myria-litre. 

Many measuring vessels are used in physical science. 
In the first book we shall only require the flask, the 
2?ij>ette, and the cylinder, described below. 

10. The flask is made to hold a definite number of cubic 
centimeters, when filled to a mark or ring on its neck. 
It is named according to the number of cubic centimeters 
it can hold. 

A litre flask holds exactly 1,000 cc. ; a 100 cc. flask 
holds exactly 100 cc. 

11. A small test tube, supported by a large cork or a 
wooden foot, and provided with a scale of cubic centi- 
meters, divided into tenths, is sufficient for common pur- 
poses. Such a tube is called a graduated cylinder. The 
scale is either etched into the glass, or marked with ink on 
a strip of paper pasted on the outer wall of the cylinder. 

To read '//'the level of the liquid in the same, bring the 
eve on a level with the concave surface of the liquid — not 
with the moisture on the wall. It is also essential that the 
tube should be vertical while reading off. A tube hold- 
ing only 5 cc. or 10 cc. is quite sufficient for many pur- 
poses. 

12. It is often required to transfer a small amount of 



Volume. 



liquid from one vessel into another without handling the 
vessels. This can be done by means of a pipette or 
dropping tube. 

A small glass tube, 1 decimeter long and 2 — 4 milli- 
meters in diameter, drawn out* at one end with a narrow 
jet, will answer very well as pipette, if only a few drops 
of liquid are to be transferred. 

Hold this pipette between the thumb and second finger 
of the right hand, insert the jet into the liquid to be trans- 
ferred, and then close the top opening with the first finger. 
The filled pipette may now be lifted out from the liquid, 
without any thereof running out of the pipette. But as 
soon as the finger is taken away from the top, the liquid 
will drop out from the pipette. 

Not all will flow out ; a column will remain in the 
pipette, especially if the jet be very narrow. This action 
of narrow tubes on liquid is called capillarity. It is so 
much the greater, the more narrow the tube. 

Practice so that the contents of the pipette drops slowly 
out in separate drops, the number of which you count. 
By dropping into the graduated cylinder, you will find that 
one cubic centimeter holds from 20 to 30 drops, according 
to the size of the pipette. 

13. At times the pipette is to transfer only a fixed quan- 
tity, say 1 go, or 0.5 cc. A notch (filed) on the tube in- 
dicates the level at which the liquid must stand in the 
pipette in order to hold this amount. By gently blowing 
in at the wide opening, even the otherwise adhering liquid 
is transferred, especially if the opening be not too narrow. 

If the pipette is to hold a larger quantity, it has a bulb 
blown in the tube. 

If the pipette is also to serve as measure, a scale is 
etched on the tube, often reading to hundredths of a cubic 
centimeter. This constitutes the graduated pipette. 

*After softening the same in a good alcohol or gas flame. See Part II. If very- 
narrow, 1—2 mm., need not be drawn out at all. To cut a glass tube, draw the sharp 
edge of a hard file across the tube ; the tube readily breaks at the place thus marked. 
The fracture is rounded off by a few strokes of the file while the tube is rotated 
between the finders. 



6 Chapter I. 



. 14. Practice. — Measure the volume of a few of the ves 
sels* near at hand, and neatly record the result in your 
journal. How to measure the volume of solids, see 30 
and 31. 

III. WEIGHT. 

15. The weight of one cubic centimeter of water is 
taken as the unit of weight, and called a gramme. 

Since water changes its bulk according to the degree of 
heat prevailing, the law establishing the metrical system 
(see 3) fixes 4° C. (four degrees centigrade, see Part II.) 
as the degree of heat at which the cubic centimeter of 
water is to be weighed. For at this temperature water is 
more dense than at any other degree of heat. 

The divisions and multiples of the gramme are accord- 
ingly (see 5) : — 

Unit 1 gramme. 

DIVISIONS. 

Vio g r • • • 1 deci-gramme. 
Vioo " . . .1 centi-gramme. 



Viooo " • • -1 milli-gramme. 



MULTIPLES. 



10 gr. . .1 deca-gramme. 
100 u . . .1 hecto-gramme. 
1,000 " . . .1 kilo-gramme. 



The abbreviations in most common use are: gr., one 
gramme ; mgr., one milligramme ; kgr., one kilogramme. 
The latter is the common unit of weight in commercial 
transactions. 

Hence, 5.21 gr. is 5 grammes, 2 decigrammes, 1 centi- 
gramme. 

16- The weights, from the gramme upwards, are usually 
made of brass. These weights are to be finely gilt, to pre- 
vent their corrosion by the air, which would change the 
weight. The general form of these weights is cylindrical. 
A projecting handle enables us to take hold of the same 
by means of small tongs or tweezers. 

The sub-divisions of the gramme are best made of 
platinum-foil, in the shape of thin, square plates. The 
corners are cut off so as to be replaced by a short side 
about 1 mm. 

*Such as test tubes, beaker?, porcelain dishes, watch glasses, etc. 



Weight. 7 

The right-hand upper corner of these weights is bent 
upwards, to permit the weight to be taken hold of by 
means of ivory-pointed pinchers or tweezers. 

17. For students' use, the following simple substitutes* 
will answer very well indeed: — 

Weights of 5, 10, 20 grammes, cut from lead bars. 

Weights of 2, 1, 0.5, 0.2, 0.1 grammes, cut from sheet 
zinc. 

A pair of common steel tweezers are used to handle 
these weights. Such tweezers can be had in every jew- 
elry shop. 

The weights are kept in a small case of wood, with holes 
for the reception of the several weights. The arrange- 
ment of the weights is usually thus : — 

Brass \ 5 2 l 1 J 

J3rass J 10 10 20 50 

Platinum... \ 0.05 0.1 0.1 0.2 0.5 

If the above substitutes are used, a piece of card paper 
(10 cm. long by 6 cm. wide) will answer well in place of 
this box, if the form and value of each weight is marked 
on the card. 

18. Each weight must, after having been used, immedi- 
ately be replaced into its own little cavity in the case, into 
which it exactly fits, or to its spot on the card. The 
weights must never be touched by the fingers, but be handled 
by means of small tweezers only. 

When weighing we read off the weight on the scale by 
noticing which weights are absent from the case or card. 
Suppose that 20, 10, 5, and 1 be out, the weights on the 
scale are 20+10, or three tens, and 5+1 units ; or the 
weight is 36 grammes, which is written 36 gr., or even 36 
— grammes being understood as a matter of course. 

This reading is entered in the student's note book, and 
while thereafter taking off the weights from the scale pan, 
the written number is carefully compared with the weights 
themselves. Only in this manner will errors be avoided. 

*How to make them, see 23. 



Chapter' J. 



19. While weighing, the weights are tried in the scale 
pan in the order of their magnitude. Thus, if we judge 
the weight to be more than '20 gr. we first put on 50; if 
too much, 20 next; if not enough, add 10; if that is too 
much, put on, 5, etc., etc. This is the shortest method of 
weighing. 

20- The common druggists' prescription scales, of 
brass, * is fully sufficient for all work connected with this 
first book in physical science. 

The scale pans rest on the marble slab, while weights or 
substance is put on the scales. Then, in order to try* the 
equilibrium, the knob on the support is turned, where- 
by the beam is raised until one of the pans, at least, is 
lifted up from the slab. If the raised pan contains the 
weights, there are not enough weights on it yet. If the 
scale pan containing the burden was raised, weights have 
to be removed from the other pan. When, finally, equi- 
librium is obtained, the pointer oscillates to equal distances 
on both sides of the middle of the short graduated arc on 
the main support. Carefully comply with 18 and 19. 

It is customary and advisable to put the substance to be 
weighed on the left scale pan, and the weights on the right 
pan. The case (or card) with the weights is placed con- 
veniently near the right-hand scale pan. 

If the above prescription scale (20) should be too expen- 
sive vet, a small pair of hand scales, costing about one dol- 
lar, will suffice for most problems in this first book. 

21. The degree of accuracy sufficient in this book is: 
fur weights to l / l0 gramme or one deci-gramme ; for vol- 
umes the same amount, or x /io cubic centi-ineter, and for 
lengths to 1 mm. That is to the first decimal. This degree 
of accuracy is easily attained by the means here described. 

In the second book an accuracy of 0.001, or one milli- 
gramme, and even 0.0001, is frequently required; hence 
there a much more delicate balance will be necessary. 



♦Silver plating Lb useless and really objectionable for laboratory purposes, since 
silver too quickly tarnishes in the laboratory. 



Weight. 9 



22. The decimal weights and measures are embodied in 
the United States five-cent nickel coin, issued according to 
the law of 1866. The diameter of these coins is 20 milli- 
meters (2 cm.), which thus enables us to make a milli- 
meter scale (7). The weight of the same coin is 5 
grammes. Thereby the pupil is enabled to make a set of 
weights and measures for his own use. See 23. 

5.142 Concrete and abstract numbers. — 

5,072 It cannot be expected that the weight of 

5.037 this coin is exactly 5 grammes. Indeed, 

5.032 by weighing, on an accurate scale, seven 

5.030 five-cent pieces, such as they came to 

4.950 hand, we found their weights as here 

4.926 given. The mean of these seven weights 

is 5.029, or 29 milligrammes more than 

Sum, 35.189 5 grammes. 

This example shows also, strikingly, 

Mean, 5.029 that, in practice, 5 is not the same as 
5.000. Hence, heware of writing down 

any decimal* not actually determined. 

23. To MAKE A SET OF WEIGHTS AND MEASURES. The 

lead weights (see 17) are easily cut out from the lead bar, 
in the shape of rectangular blocks with the edges cut off. 
First make a weight equal to the five-cent piece ; then put 
this with the coin, and balance both, thus obtaining the 1§ 
gramme weight, etc. 

The smaller weights are made from zinc sheet. Cut out 
a rectangular piece, 1 cm. wide, and trim its length until 
it balances the 10 grammes. Measure this length ; cut off 
Hub Vio> Vio* 2 /io, 5 /io> and you have the weights 1, 1, 1, 2, 
5 grammes. 

Similarly, you can make the necessary 0.1, 0.1, 0.2, and 
0.5 weights. 

Finally, by weighing water in a tube (see 11), we get 
from the same coin the weights made therefrom, or the 
graduated vessels for measuring volumes. The amount of 
water balancing one live-cent coin is evidently 5 cc. To 
obtain the scale (11), we need only mark the level of the 
water when enough has been poured in to exactly balance 

*The zero 0.0 included. 

2 



10 Chapter L 



1 gramme, 2 grammes, 3 grammes, etc., until 10 grammes, 
and finally to divide the intervals in equal parts to tenths. 

24. Practice. — The student must weigh several bodies 
close at hand, such as small blocks of wood, pencils, pens, 
etc. The result must be neatly entered in the student's 
journal. 

Examples. — Try delicacy of balance. How much turn 
for 0.1 gr. when both pans are empty, or when each con- 
tains 10 gr. ? Accuracy for beginner, 0.05 gr. Weigh sev- 
eral five-cent pieces (nickel). Weigh several other small 
bodies. How much uncertainty in each case ? Make a 
set of gramme weights of zinc sheet (2, 1, 0.1). Make a 
like set of lead rods (5, 10, 20 gr). 

IV. SPECIFIC GRAVITY. 

25. The weight (in grammes) of one cubic centimeter 
of any substance is called the specific gravity of the same, 
and usually denoted by the letter G. 

26. Thus one cubic centimeter of water weighs one 
gramme (see 15) ; hence the specific gravity of water is 
one. One cubic centimeter of lead weighs 11.4 grammes ; 
hence the specific gravity of lead is 11.4. The specific 
gravity of gold is 19.3; of mercury, 13.6 — that is, one 
cubic centimeter of gold weighs 19.3 grammes; the same 
volume of mercury weighs 13.6 grammes. 

Practice. — Weigh a cubic centimeter of cork, wood, 
lead, iron, chalk, etc. 

27- The specific gravity (G) of any substance can, there- 
fore, be calculated by dividing its weight (w) (in grammes) 
by its volume (v) (in cubic centimeters): — 

V 

This fraction evidently gives the weight of one cubic 
centimeter (in grammes) ; that is, the specific gravity. 
For if v cubic centimeters weigh w grammes, one cubic 
centimenter weighs J /v of w, or w / v grammes. 



Specific Gravity. 11 



28. Practice. — Take several square blocks of wood, 
cork, etc. By measuring the three dimensions, 1, b, h, (see 
1) by the centimeter scale (see 8), we obtain the volume, v, 
in cubic centimeters as the product of the three dimen- 
sions : — 

v=l. b. h. cubic centimeters. 
Then weigh the block ; this gives w grammes. Then 
calculate the fraction : — 

V 

29. If the substance be a liquid, pour some of the same 
into the graduated cylinder (11), the weight of which has 
first been ascertained (=a). Weigh the cylinder with the 
liquid (=b) ; then the difference (b — a) is the weight w of 
the liquid in the cylinder. JSTow read off the level of the 
liquid ; we thereby ascertain v, its volume in cubic centi- 
meters. Theu w divided by v gives the specific gravity, G. 

Carefully clean and dry the cylinder before and after 
use ! Use a small stick, some blotting paper, a rag, etc. 
A few liquids are kept in small bottles (50 — 100 cc.) for 
this practice exclusively. Liquids very suitable are: 
Water, alcohol, gasolene (be careful, keep far from the 
flame), kerosene / also, some saturated solutions of differ- 
ent soluble salts.* 

30. If the substance be a solid, break it up into pieces 
that can easily be dropped into the cylinder. Fill the cyl- 
inder with water up to about 3 or 5 cc. ; accurately read off 
the level of the water, (let it be a cc.) Then weigh the 
body ; thus we have w. Drop all the weighed pieces 
gently into the cylinder (held somewhat inclined, to pre- 
vent loss of liquid), and read off the level of the water 
again (=b). The number of cubic centimeters b — a which 
the water rose is evidently equal to the volume of the sub- 
stance dropped into the water; that is, v=b — a. Hence 
the specific gravity is f= b ~. 

*Mercury is too dangerous for beginners to handle. 



12 Chapter L 



If the substance is soluble in water, take gasolene in 
place of water. Remember that gasolene is highly inflam- 
mable and dangerous ; so remain at very great distance 
from flame or fire while handling this liquid. 

The solids used for this purpose are kept in small speci- 
men tubes of about 5 cc. capacity, and properly labeled. 
The material is best in the shape of coarse fragments, of 
about J to \ cc. 

As good examples, take : Glass (pieces of glass rods), 
sulphur, iron (nails), copper (sheet), zinc (sheet), lead (shot 
or pieces). The above are all insoluble in water. 

In gasolene you determine, for example, nitre, blue 
vitriol, alum. 

Always carefully dry each substance before putting it 
back into its glass tube. 

31. The degree of accuracy of the specific gravity thus 
determined is easily ascertained. Let the possible error in 
the determination of the weight w be e, and the possible 
error in the determination of the volume v be e'. Then 
we only know that the weight is some value between w+e 
and w — e, and the volume some value between v+e' and 
v — e'. Hence the specific gravity is some value between 

w+e w — e 

, and — ; — i 

v — e' v+e 

By calculating these two limits in any given case, you 
can ascertain the reliability of the specific gravity deter- 
mined. You will thus find that you hardly ever need cal- 
culate more than one decimal, if you use the balance and 
cylinder here described. 

The balance used above weighs accurately to the deci- 
gramme, or to the first decimal; hence the greatest possi- 
ble error in weight is e=0.05 grammes. Since the cylin- 
der is divided into tenths of cubic centimeter, the greatest 
possible error in the determination of the volume is also 
e'=0.05. Hence the specific gravity will ordinarily be in- 
cluded between the limits, — 

w— .05 w+0.05 

V+0'M < < v— 0.05 

32. Gases are much lighter than solids. The numbers 
expressing their specific gravity according to 25 are, there- 
fore, very small. The smallest of all these values is that 



Appendix. 13 



for hydrogen, which is 0.0000896 ; one cubic centimeter of 
hydrogen weighs only this fraction of a gramme. 

We state here only a few of the results obtained; in a 
subsequent book the weighing of gases will be treated of 
in detail. 

33. It is very convenient to take this weight of one cubic 
centimeter of hydrogen as a new unit, called one crith. 
Then the specific gravity of hydrogen is one (crith). That 
of common atmospheric air is 14.4 crith. One cubic centi- 
meter of air is found to weigh 14.4 times as much as the 
same volume of hydrogen ; for it weighs 0.0012932 
grammes. 

34. The greatest specific gravity of any yet found is 
that of iridium ; it is 21. That of the gas hydrogen is the 
smallest; it is 0.0000896 only. Iridium, the heaviest sub- 
stance, is hence almost 300,000 times more dense than 
hydrogen, the lightest body known. 

Bodies thus differ very much in specific gravity. 

APPENDIX. 

35. Angles. — The circle is divided into 360 equal parts, 
called degrees, by straight lines drawn from the center. 
Each degree is again divided into 60 equal parts, called 
minutes. 

For practical purposes, the divided circle is drawn on 
paper or engraved in horn or metal (brass, German silver). 
The simplest divided full or half circles are called pro- 
tractors / they are sufficient for the beginner. More elab- 
orate divided circles are used in surveying, practical astron- 
omy, and the different branches of physics ; they are part 
of theodolites, transits, compasses, spectroscopes, etc. 

36. The simplest goniometer consists of two pieces of card- 
■ board, each 1 dm. long, 1 cm. wide, and centered by a 

short pin. By putting a small piece of india-rubber on the 
pin against the card, the hinge acquires firmness. 

The two cards of this goniometer are made to include 
the angle which is to be measured. By then applying the 
goniometer on the protractor, the .number of degrees of 



14 Chapter I. 



the measured angle may be read off. Or the angle may 
be transferred to paper. 

37. Time. — At any given instant, mark the line of 
shadow which a vertical rod in the sun-light throws on the 
ground. The time which elapses till the shadow returns to 
the same line is called a day — so that the day is the dura- 
tion of one (apparent) revolution of the sun around the 
earth. 

This duration of the day is divided into 24 equal parts, 
called hours / each hour is again divided into 60 equal 
minutes, and each minute into 60 equal seconds. 

Clocks have been made to accurately indicate the time 
in hours, minutes, and seconds. 

38. A simple pendulum consists of a ball, suspended by 
a fine thread or twine. The length of the pendulum is 
the distance from the point of suspension to the center of 
the ball. 

To find this length of a pendulum, first' measure the 
diameter of the ball ; then measure the distance from the 
point of suspension to the lower extremity (tangent) of the 
ball, and finally subtract one-half the diameter of the ball 
from this length. 

When the pendulum is at rest, the string marks the ver- 
tical line. The pendulum may, therefore, be used as a 
plumhline. A line or plane at right angles to the vertical 
is said to be horizontal. The free surface of water, mer- 
cury, or any other limpid liquid, is horizontal. 

39. When the simple pendulum has been slightly re- 
moved from its position of rest, it will oscillate for a long 
time, the ball rising on eacli side of the vertical to nearly 
the same height. The time of oscillation is the duration 
oi the motion of the pendulum from its greatest distance 
from the vertical on the one side till it reaches the greatest 
distance on the other side of the vertical. 



Mensuration. 15 



The time of oscillation is found to be exactly one second 
if the length of the pendulum is 99. i centimeters (very 
nearly a meter). A pendulum of this length is called a 
second-pendulum. 

40. The fundamental quantities occurring in nature 
have now been enumerated. All other quantities depend 
upon the above. 

Before proceeding further, it is well to get practically 
acquainted with the rudiments of some branches of math- 
ematics not usually taught in the common schools — such 
as the graphical solution of geometrical problems, the use 
of co-ordinates to represent relations ; also review the prin- 
ciples of mensuration of lines, areas, and volumes. 

V. EXERCISES I3ST MENSURATION". 

41. MENSUEATION OF LENGTHS. 

Models used. — Six or eight straight wires, cut from the 
same piece, and from 1 to 20 cm. long ; kept in a paper en- 
velope. The teacher may have several sets of such wires, 
some of iron, others of lead wire, and also of different 
thicknesses, but not less than 1 mm. thick. As stated 
above, in each separate set, the wires must be cut from the 
same piece, so that they all have the same thickness. Also 
put with each lot one or two wires (cut from the same 
piece), which are bent, so that their length cannot accu- 
rately be measured directly. 

Students work. — In your note book give the above head- 
ing ; enter the date ; describe the kind of wire used ; ar- 
range them in order of their length ; call them No. 1, 2, 
3, etc. ; draw 5 vertical lines in your note book, to form 6 
columns ; draw line across the same ; enter the headings, 
No., 1, w, w / 1? w', e. 

Under No. mark the number of each wire. Then meas- 
ure each wire, and enter the length found under 1 ; go to 
the balance, weigh each wire, and carefully enter each re- 
sult under w ; then return to your desk, and for each wire 



16 Chapter L 



calculate the average weight per centimeter, or w /i; enter 
the result to two decimals, in the column so headed. 

If there was no irregularity in the wire, and if the weigh- 
ings and measurings had been perfect (as supposed in ab- 
stract mathematics), then the values in this column would 
all be identical. But since you had to deal with real 
bodies, and the accuracy of your work was only 0.05, the 
quotients will, at best, agree only in their first decimal. 
But the quotients calculated differ no more than the errors 
of your working ; hence you have established the law that 
the ic eight (w) of different pieces of the same wire is pro- 
portional to the length (1). 

It is true this result is almost self-evident ; but this sim- 
ple case fully exemplifies how physical laws are established 
by actual observation. 

Take the mean of all values of the quotient and call this 
mean c ; for it is the constant value to which the above real 
values approximate. 

If now this weight c be taken as the most reliable 
weight of one centimeter, then you can next find the 
weight w' of 1 centimeters of the wire by calculation : — 

w'=c. 1. 

Enter the values thus found in the fifth column. These 
calculated values w' should be the same as the weights w 
directly observed, if the real work was not subject to a lim- 
ited accuracy and to errors. 

Subtract the calculated value w' from the observed value 
w, and enter the difference 

e=w — w' 
'/•, in the last column. 

The more accurate all work, from the models to the cal- 
culations, the less will be these "errors" or deviations. 

Remarks. — In " pure sciences," such as the abstract 
geometry and mathematics of our schools, no such devia- 
tions are recognized. The real work, however, from the 
building of a vertical wall, to the construction of a railroad 
bridge and the adjustment of a chronometer, are subject 



Mensuration. 17 



to just such deviations between the abstract thought and 
the concrete reality. The student should early become 
acquainted therewith, and learn to ascertain the probable 
limit of the magnitude of the errors / because only if this 
limit is known, we know the degree of accurrcy we have 
attained to — or, in other words, we know how much reli- 
ance should be given to the final result* 

42. General results. — The lengths cut off are mutually 
different; so are the weights found. Quantities which 
thus change or vary together from one case to another are 
called variable quantities ', or simply variables. The quo- 
tient c did not change ; such a quantity is called a constant. 

By w'=cl. you find the value of w' by means of the 
value of 1 ; hence, in this case, w' is called the dependent 
variable, while 1 is the independent variable quantity. 

Any such equality between different quantities, ex- 
pressed in a general way (by letters, etc.), is termed an 
equation. Translate the equations occurring in 41 into 
words. 

Conclusion. — In this simple exercise we have exempli- 
fied the method of physical research, as it is used in mod- 
ern science. First we obtained, by direct observation, both 
variables, weight, w, and length, 1; thereafter we found 
that these variables were dependent one on the other, for 
w divided by 1 was (approximately) constant. We then 
'eversed the operation, by considering this relation an es- 
tablished fact, a law. The mean value of the constant c 
was multiplied by the length 1, and thus the weight w' ob- 
tained by calculation. We finally compared these calcu- 
lated values with those obtained by direct observation, 
and thus ascertained the degree of accuracy of our work in 
the values of e, by which w' differs from w. 



*Thus, a surveyor may report the area of a meadow measured by him with three 
*r four decimals attached to the number of acres. You need only to have the 
neadow re-measured in order to learn what confidence these decimals deserve. 



18 Chapter L 

If we had put one of the wires aside, and now measure 
the same, we can calculate its weight ; or, if we weigh the 
same, we can calculate its length. Thus a law once estab- 
lished is applied to the determination of unknown quanti- 
ties. Try it for the curved wire of the models. 

43, PRACTICAL MENSURATION OF AREAS. 

Models used. — Various geometrical figures, such as tri- 
angles, parallelograms, and other polygons of different 
shape and size, and a few irregular curvilinear forms, all 
cut from the same piece of sheet zinc or sheet brass.* 
The greatest dimension used should be about 15 cm. 
Keep 6 to 10 such models in an envelop of strong paper, 
and hand this to the student to work with. The teacher 
must first have ascertained that these models are really all 
of uniform thickness, or that their weight really is propor- 
tional to their area. Also have the models in each pack- 
age numbered, for the sake of reference. 

Students work. — Enter the proper heading and date in 
your note book ; state the material of the models ; take up 
the models in order of their number; describe each model 
under its own number, by giving the name of the form 
and its dimensions, as resulting from your own measure- 
ments. You best also carefully make a sketch of the model 
in your note book, letter its corners A, B, C, etc. ; draw 
necessary diagonals, etc., with dotted pencil lines, on the 
sketch, etc. Then you simply record the dimensions by 
enumerating the same on the right of the sketch by letters, 
as for instance : — 

AB=15.3 cm. 
B C=7.6 cm. 

Then calculate the area a from these measurements. For 
this purpose remember the following: — 

1. The area a of any rectangle or any parallelogram is 
the product of its base, b, and its height, h. a=b h. 

*Be careful to hare these figures cut accurately, and from the middle of the sheet; 
the margins are usually different in thickness. 



Mensuration. 19 



2. The area of any triangle is half the product of its 
base into its height. a=J b h. 

3. Any other polygon you must suppose divided into 
triangles, and then measure the base and height of each of 
these triangles ; the sum of the areas of all these triangles 
then constitutes the area of the given polygon. Since 
each polygon can be supposed to be divided in two and 
more sets of such triangles, you can check your work, by 
making at least two independent determinations for each 
polygon.* 

Next weigh the model ; this gives w grammes. Then 
divide w by a, which gives you the calculated weight for 
each square centimeter. 

Do all this with each of the models. Then sum up the 
results in a table of seven columns, containing, from left 
to right: .Number, name, area (a), weight (w), weight of 
one square centimeter ( w / a ). 

The last values are again all nearly equal, if the material 
for the models had been carefully selected. Therefore take 
the mean of all these values ; call this c. Then calculate 
the weight w'=c. a. ; enter this value in the sixth column. 
In the seventh place the error e=w — w'. See 41 and 42 
for further explanations. 

If this work has been done carefully — as all work must 
be done — these errors will be found to be but small. You 
may then calculate the area of the irregular and curvi- 
linear models in the envelop, by weighing the same, and 
dividing the weight by c. Why ? 

44. MENSURATION OF THE VOLUME OF SOLIDS. 

Models used. — From the same piece of wood have care- 
fully made several blocks, such as cubes, square and ob- 



*In order to simplify this work, the teacher better accurately scratch the di- 
viding lines in the model by means of a sharp point. The two sides of the model 
thus give the two sets of divisions ready for students' use. On the one side you 
may divide by diagonals only, giving scalene triangles ; on the other, by one diag- 
onal and perpendiculars thereto, so as to divide this side of the polygon into 
right angled triangles and trapezoids. 



20 Chapter L 



lique parallelopipeds, prisms of various shapes, and also 
pyramids ; finally again a few more or less irregular bodies, 
which it would be nearly impossible to directly measure. 
The greatest dimensions need not exceed 10 or 15 cm. 
Keep a set of such blocks in a wooden box ; have the 
blocks in each box numbered. 

The student's work is now precisely as in the preceding 
exercise — only that here he measures the base (b), by the 
process given in that exercise, and then measures the 
height (h), whereby the square rule often is of great use. 
He then must remember : — 

1. The volume (v) of any prism is the product of the 
base and the vertical height. v=b. h. 

2. The volume (v) of a pyramid is one-third the product 
of the base into the height. v=£ b. h. 



45. Application of these methods to Elementary Geome- 
try. — The propositions demonstrated in abstract geometry 
may readily be established as physical facts by means oi 
the balance and good models cut from sheet metal. W& 
shall give but a few of these important exercises for begin- 
ners, and for those more advanced students who have had 
no practice. 

46. THE AREA OF SIMILAR FIGURES IS PROPORTIONAL TO 
THE SQUARE OF THEIR HOMOLOGOUS LINES. 

Models. — Also here several different sets of four to 
eight models each, may readily be procured by the teacher; 
say one set of squares, another set of similar triangles, 
and a set of similar bat quite irregular pentagons — each 
set kept in a separate strong envelop. 

Student's work. — The student, having received some 
one set, enters the usual preliminaries in his note book, and 
thereafter first convinces himself that the figures are really 



Mensuration. 



21 



similar; secondly, determines their weight ; finally, finds 
the relation between this weight and the homologous di- 
mensions. All models having been cut from the same uni- 
form sheet zinc, these weights are proportional to the area, 
as has been shown in 43. 

For the sake of completeness, it is well to have a rec- 
tangle, say 2 by 5 centimeters, to directly determine the 
weight c of one square centimeter, in order to actually re- 
duce the observed weight w to the area a by dividing w 
by c for each model. (See 43.) 

First, to ascertain whether the models really are similar 
figures, the student enters a carefully drawn sketch of any 
one of them in his note book, and letters the corners in this 
sketch for sake of easy reference; then places all models 
before him in a like position, so that the homologous parts 
will be denoted by the same letters. 

Hence the homologous angles must he equal, and homolo- 
gous lines must he proportional, in order that the figures 
may he similar, (Definition.) 

The student ascertains the equality of the angles by 
direct superposition ; and states the results of his observa- 
tions in the note book. 

To ascertain the proportionality of the homologous lines 
requires more work. First measure on one model as many 
lines, such as the sides, A B, B C, C D, etc., and diagonals, 
A C, A D, A E, etc. ; also B D, B E, etc. etc. — in fact, as 
many as are deemed necessary. Enter these results in a 
table like this : — 

LENGTHS IN MODEL. 



Line. 


No. 1 


No. 2 


No. 3 


etc. 


AB.... 










BC... 











Etc. 



No. 2 No. 3 No. 4 


No. 1 No. 1 No. l| 



22 Chapter L 



Then divide all these values by the values found for any- 
one, say for No. 1; enter the quotients or ratios thus ob- 
tained in a like table, under the heading, — 



etc. 



Then, if the figures investigated are really similar, the 
ratios in any one vertical column must be very nearly the 
same. You can draw a line below, and take the mean of 
each. This, then, is the most exact value of the ratio be- 
tween the homologous lines in No. 2 and No. 1, No. 3 and 
No. 1, etc. Of course you might also determine, in the 
same manner, the ratios No. 4, No. 2, etc. etc. 

Next multiply these ratios by themselves, and enter this 
value as the square of the ratios below the ratios themselves 
at the foot of the columns. Draw another line across the 
table. Weigh each model, and enter the result in your 
note book. Divide these weights in the above manner, 
such as weight of No. 2 divide by weight of No. 1, etc. 
Enter these ratios of weights in the corresponding table ; 
or, better, repeat the form of table, enter the ratios of 
weight, and mark the ratios above found, as well as their 
square, below the same. 

You will then find that the ratios of weights are very 
nearly the same as the squares of the ratios of homologous 
lines. Since now weights represent areas, the geometrical 
proposition above stated has been proved to be a physical 
fact. 

If you- choose, you may reduce each weight to area, and 
find the ratio of areas instead of the ratios of weight. 

47. TIIE VOLUME OF SIMILAR POLYHEDRA IS PROPORTIONAL 
TO TIIE CUBES OF THEIR HOMOLOGOUS LINES. 

This exercise may be conducted in precisely the same 
manner with wooden blocks, kept in a box. The simplest 
shape of the blocks is the right-angled tabular form. 



Mensuration. 23 



48, TO DETERMINE THE RELATION BETWEEN THE AREA OR 
THE CIRCUMFERENCE OF A CIRCLE AND ITS RADIUS. 

Models.— From homogeneous zinc or brass sheet, have, 
as accurately as possible, cut four to eight different circles, 
the radii of which range from 1 to 5 centimeters ; also a 
rectangle of exactly 2 by 5 centimeters. 

Studenfs work. — Weigh the latter; then exactly one- 
tenth of this weight is the weight of one square centime- 
ter of the plate used. Call this weight c. 

Enter this, together with the usual preliminaries, in your 
note book. Then construct a table like the the one in 46 ; 
mark the vertical columns (after the first) with the number 
designating the model. In the first column enter first 
line, r=radius. Measure the length of the radius of 
each plate carefully ; enter the result at the proper place 
in the table. Multiply each radius by itself to form its 
square; enter these results below the former in the next 
horizontal line, which you mark r 2 (that is radius square). 

Next determine the weight w of each plate ; enter these 
values in the third horizontal, marked w. Then calculate 
and properly enter the area a of each circle ; that is, — 

w 

a=- 

c 

a a 
Now calculate the ratios - and - for each circle ; enter 

r r 2 

the results as before, in the next horizontal lines. 

Tou will then find that the area divided by the square 

of the radius is for all circles very nearly the same, or a 

constant quantity / it is 3.14. Consequently you have — 

a 

or the area a of any circle is obtained by multiplying the 
square r 2 of the radius by 3.14. This constant ratio is 



24 Chapter I. 



termed pee, and usually denoted by the Greek letter ^cor- 
responding to the English p. That is, if tt=3.14 — 

a=7r. r 2 . 
It is easily shown (if need be by the teacher) that the 
area a of the circle may be considered as composed of an 
immense number of small triangles, the base of each of 
which is a very short part of the circumference ; while 
the height of all is equal to the radius. Hence we have 
a=£ 0. r. Since also a=;r. r 2 , we have ?r. r 2 =^ C. r., and 
consequently — 

C=2 tt. r. 

The circumference of any circle is tt=3.14 multiplied by 
double the radius {i. e. the diameter). 

Note. — With glass balls of different sizes it is easy, in a 
like manner, to determine the volume v and the curved 
surface s of a globe. Tou w 7 ill find — 

v=f it. r 3 . 8=4. tt. r 2 . 

How far do 46 and 47 cover the ground of 48 ? 

49. PYTHAGORAS'S THEOREM. 

This famous and important proposition of pure geometry 
is readily established as a fact by any model prepared in 
the following manner: — 

With a sharp point, draw any right-angled triangle on 
good, uniform sheet metal (zinc or brass.) Construct the 
square on each side, all outside the triangle. r Cut out 
the figure very accurately.* Put the square of the hypothe- 
nuse on the one scale pan, the squares of the sides together 
on the other scale pan of a balance. You will find that 
there is equilibrium. Hence the above proposition is a fact. 



*This model in a strong envelop, is given to the student, who merely verifies 
the figure by puttting the parts together. Then he passes to the balance. 



Linear Drawing. 25 

50. CONCLUSION. 

The preceding must be sufficient to show both the im- 
portance of this kind of very simple practice in making the 
student familiar with magnitude and its investigation, and 
to show that such practice should precede the abstract 
study of pure geometry. But, at any rate, this kind of 
work forms-the simplest possible introduction to the meth- 
ods of modern research in physical science. Hence the 
student who faithfully completes even this short course of 
exercises will be excellently prepared to begin the thor- 
ough study of physical science. 

VI, EXEBCISE3 IN LINEAB DRAWING. 

51. The school should furnish the class with the follow- 
ing simple drawing tools : — 

1. Square rulers, of wood ; 20 cm. long, 4 cm. wide, 
0.3 cm. thick. None of the edges should be beveled. 

2. Triangles, of wood, the two sides of which should be 
10 and 5 cm. at least. 

3. A few pairs of brass dividers. 

4. Some horn protractors. 

5. Millimeter scale, on card paper (see fig. 1, plate 1) ; 
and, for the more accurate work : — 

6. Some proportional scales, 10 cm. long, with an addi- 
tional centimeter divided into tenths, and by diagonals 
into hundredths. This scale may be pasted upon one side 
of the rulers. 

If the work is properly distributed among the members 
of a class, only a few sets of the above tools are required ; 
besides, students should be encouraged to purchase a set 
of the above tools for their own use. 

52. Each student must provide himself with white, un- 
ruled paper, which should not be rolled, but always be 
kept flat. A few sheets may be folded to common quarto 
size (about 20 cm. square) and protected by a cover. The 
student's drawing pencil, of medium hardness (No. 3), 



26 Chapter I. 

should be most carefully sharpened,* so that the graphite 
forma a sharp edge} it should be exclusively used . for 
drawing. 

53. Draw straight lines, by holding the pencil nearly 
vertical and with its edge close to the ruler. The line 
must be continuous, of equal width, but quite fine, so 
that it is merely distinctly visible. It should be less than 
x / 6 mm. For practice, draw a system of parallel lines 
alono; one edge of the triangle, which you hold by means 
of the first and second fingers firmly against the edge of 
the ruler — the latter held quite firm by means of the re- 
maining fingers of the left hand. After drawing a line 
with the pencil in the right hand, slide the triangle from 
the line far enough to give place for a new line. Continue 
this until you have drawn ten or twenty such lines, all as 
near as possible to one another, but also equally distant. 
When done, ascertain how many lines have found place 
in ten millimeters, or what fraction of a millimeter the 
lines are apart. 

This exercise exemplifies that a line is drawn parallel to 
any given line through any point by sliding the triangle 
along the ruler, as above. 

54. A point is marked on a line by drawing the edge 
of the pencil across the line, or by very gently pressing 
the point of the compasses into (not through) the paper. 
Since so faint a mark would be easily overlooked, and 



♦To sharpen the pencil, first cut the wood, then the graphite. To cut the wood, 

hold the pencil in your hit hand, between the thumb and first finger, but resting 

:d joint of the second finger. Grasp the pen-knife with the right hand, 

put the pencil on the thumb of the right hand, and cut the wood so as to form a six- 

i pyramid of not ten than two centimeters in height. 

lrpen the graph obtain an edge proper for drawing, take the pen- 

D your left hand, the palm turned upwards, pressing the pen- 
cil between the thumb and the second, third, and fourth fingers of the left, so that 
the first finger (pointer) remains f;<e. Gently support the point of the pencil on, 
or rather fa, the Boft, upwards-turned, last joint of this finger, and gently scrape th« 
ith the sharp pen-knife, only od the one side exposed. Then turn the pencil 
ono-half around (180°;, and scrape the side now up. Thus a vharp edge will be pro- 
duced, fit for accurate drawing. 



Linear Drawing. 27 

ir."-:!: time lo-t in --•Hzl :Lt ^ame ::: :'t::t"_e: use, a small 
::r millimeter in diameter, is drawn around 
it in band In this manner all points are 

marked on good drawin — 

55. A circle maybe faintly scratched into the paper 
by one point =, ~h:ir the other is held in the 

31 of the circle : a few gentle pencil dots may then 
carefully be e 1 along the curve thus Or you 

may use a pair of dividers, one point of which consists of 
ened pencil. 
The radinfi of any eircle is equal to the side :: the reg- 
ular hexagon inscribed in ti le circle — or the chord 
of 60 degrees is equal to the radius. Convince you: 
of this fact by actual drawing, carefull v marking the 
points in the tie length oi the 
radius. This exercise is also a good test for the accuracy 
tally if you draw the three dnpnetere 
and the six sides of the hexagon; lor any two opposite 
sides must be parallel to the ; ining the other four 
sides. Try whether they are para: irawing(53). 

56. The student should also practice the use of the pro- 
or. Keep the side on which the divisi n lines are en- 
graved in co: ;. Draw angles, and :: 

heir magnitude by means of this protractor. Also 
inversely draw angles of a given number of degrees, say 
of 20, i'J. 45, etc, :;e_rccS. Test your work in van 
ways. 

57. The sum of the there. .-. J.. B, C, in any tri- 
angle A. B. C\ is eouerf ie> 1S0 C . or to two rioht aecles. 

Draw any three straight lines (fig. 3), two and tw inter- 

g one another ; mark the points of intersection A, 

B, C ; measure these ngles by means of the protractor ; 

add these three angles ; divide the sum by 180°. The 

quotient then will differ but very little from unity. 

Find the error committed, that is, the difference be- 



28 Chapter I. 



tween the above quotient and unity. The more careful 
your drawing and measurement, the less will be this error. 
Ilonce the above proposition a fact. 

None of the sides of this triangle should be less than 2 
cm. All sides should be sufficiently produced, in order to 
be able to accurately measure the angle. 

If two angles in a triangle are given, can you then find 
the third angle? How? If the triangle is right-angled, 
how great is the sum of the other two angles ? 

The complement of any angle, added to the angle itself, 
gives 90 degrees ; the supplement added gives 180°. 

58. Draw a line, B C, at right angles 'to another, A C, 
(fig. 4) ; intersect these lines by any third line, B A, so as 
to form any right-angled triangle, AOB. Carefully 
measure the sides AC — b and BC =a(to the hundredth 
of the centimeter) ; also, the hypothenuse AB = c. Mul- 
tiply each of these lengths by itself, (that is, calculate the 
square) of each side a, b, and of the hypothenuse c (leav- 
ing but two decimals in the result). Divide the sum of 
the squares of the sides by the square of the hypothenuse; 
that is, calculate the quotient : — 

a 2 +b 2 

2= 

c 2 

You will find this quotient very nearly equal to one. 

You may draw another line, A B, across C A and C B, 
so as to obtain another right-angled triangle (No. 2), and 
repeat all the operations. You will thus obtain another 
value for q. 

This you may repeat for several more lines A B. You 
will always find the quotient nearly equal to unity; and 
the more careful your construction and measurements, the 
less the difference between the quotient and unity. Hence 
this difference must be considered the error of the practi- 
cal work, so that [Pythagoras' Theorem] : 

The square of the hypothenuse of any right-angled tri- 
angle is equal to the sum of the squares of 'the two sides. 

If a = 3, b = 4, how great c ? 



Linear Drawing. 29 



Compare 49, where this same geometrical proposition is 
proved by the balance. 

59, The construction of a triangle from given quanti- 
ties is very important, for by such construction a great 
many problems of physical science can readily be solved. 

A triangle (fig. 3) contains, in all, six pieces ; viz : three 
angles, A, B and C, and three sides, a, b, c. But since 
any two angles determine the third } by 57, there remain 
only five pieces in eaxh triangle, of which any three are 
sufficient to determine the triangle. 

We shall use the letters A, B, C, to denote the magni- 
tude of the angles, and a, b, c, to denote the magnitude 
of the sides ; side a being opposite angle A, etc. — pre- 
cisely as in fig. 3. It will be sufficient to give for each 
case general directions for the mode of construction, 
which the student should carry out with the special values 
given for each of the pieces at the close. The teacher 
may add other special values, if there is time for the 
work. 

All these constructions must be performed with great 
care and accuracy ; the result is to be reported to the 
teacher ; for the sides, to the second decimal of the cen- 
timeter, and for the angle to the fourth or sixth part of 
a degree. The teacher will then, by telling the student 
the true result, convince the student of the degree of 
accuracy attained. 

We now proceed to the four cases possible in the con- 
struction of triangles : — 

60. Case I. Given the three sides, a, b, c / to find the 
angles A, B, C, of the triangle {fig. 3). 

Draw a line ; cut off AB = c ; with given side b as 
radius, describe an arc of a circle around point A as cen- 
ter ; with given side a as radius, describe an arc of circle 
around point B as center ; the point of intersection of 
these two arcs will be C ; mark it so, and join it by 
straight lines with the points A and B. Then ABC is 
the triangle required. 

Now, by means of the protractor, carefully measure the 
three angles, A, B, C. 



30 Chapter L 



Example 1. Given a — 9.46, b= 8.03, c = 8.24 cen- 
timeters. Find A, B, C. 

61. Case II. Given two sides , c, h, and the included 
angle A / to find the third side a, and the other two angles, 
B, C, of the triangle {fig. 3). 

Draw a line ; cut off AB = c ; draw through point A 
a line A C, forming with c the given angle A; cut off AC 
= b on this line ; join C with B. Then ABC is the 
triangle sought. 

Measure CB = a, and also the angles C and B. 

Example 1. Given b = 5.65, c = 3.80 centimeters, 
and A = 64 1 / 6 degrees. 

62. Case III. Given two sides, e and a, and an oppo- 
site angle, A / to find the third side, h, and the two angles, 
B, C, of the triangle {fig. 5). 

Draw a line ; cut off AB = c, draw a line AC, form- 
ing with A B the given angle, A ; around B as center, 
describe a circle with radius equal to a. You will then 
find either one of the following cases : 

1st. This circle does not intersect the line A C ; hence 
no triangle can be formed by the three given pieces, or 
the problem is absurd. 

2d. This circle does exactly touch the line A C in the 
point C ; hence the triangle sought is a right-angled tri- 
angle. 

3d. This circle intersects the line A C itself in two 
points, which you mark C and C. Join each of these with 
B, and you will have two different triangles, ABC and 
A B C v , which both contain the three given parts. Hence 
in that case the problem gives two distinct solutions. 

4th. This circle intersects the line A C only in one 
point C, above A B (and the line A C produced towards 
C" ', below A B). In that case the problem has but one so- 
lution, A B C. 

Whichever of these last three cases obtains, you meas- 
ure the third side, A C (or A C') = b, and the two angles 
B and C (or C.) 

E 'ample 1. Given a = 4.16, c = 3.26 centimeters, and 
ande A = 68f degrees. 

Example 2. Given a =2.12, c — 8.36 centimeters, and 
angle A — 14^- degrees. 



Linear Drawing. 31 



63. Case IV. Given one side, <?, and two angles y to 
find the other two sides a, 5, and the third angle of the tri- 
angle {fig. 3). 

Add the given two angles and subtract the sum from 
180 degrees ; the difference will be the third angle (com- 
pare 57). Then draw a line; cut off AB =c; through the 
point A draw a line forming the angle A with::,c ; through 
the point B draw a line forming the angle B with c; 
the point of intersection of these^. two lines will be C, 
and ABO, the triangle required. 

Measure A C = b and B C = a. 

Example 1. The side c = 14.4 cm. and angles'A = 60, 
B = 35J degrees. 

64. In the right-angled triangle, one angle is 90°, say 
= 90°. Hence there remain only four pieces (compare 
59), so that only two pieces need to be given in order to 
find all the other pieces of the right-angled triangle. 

Examples are readily solved. 

DRAWING TO SCALE. 

65. Similar figures are such as have homologous an- 
gles equal, and homologous lines proportional. Lines or 
angles are said to be homologous, if they correspond to 
each other in these figures in position. Compare 46, 
where this definition has been used. 

66. The art of drawing to scale reproduces in the 
drawing a figure similar to the figure of the original ob- 
ject. If this object be large, the figure is drawn smaller 
than the object, so as to find room on the paper. If the 
object, however, be very minute, then the drawing is 
made larger than the object, in order to distinguish the 
parts readily by the naked eye. 

The ratio between the length of any line in the drawing 
and the homologous line in the object is called the scale 
of the drawing. It should always be plainly marked on 
each drawing. Thus if a drawing is marked : Scale J, we 
know that each line in the drawing has exactly one-half 
the length of the corresponding line in the object. 



32 Chapter L 



very much used are Scale 1 / 6 to l / 10 for smaller 
objec hau one meter in dimension. Scale 1 / 100 for 

large buildings, etc. Scale Viooo for large fields, etc. 
Mwps of a State.of moderate size may be drawn to scale 
Viooooo ; larger States to scale Vi-oooooo ; a continent to 
scale l / iojooojooo? if the map is to be 20 cm. square. 

Microscopic objects are drawn to scale 10 /x, 100 / l5 1000 /i, 
30 /i, 500 /i, as the case may be. 

The following two simple exercises will introduce the 
student to the important art of drawing to scale. 

67. Triangles are similar if their homologous angles 
are equal. Figure 6. 

Draw any triangle, ABC, the sides of which are not 
less than 2 cm. Draw any line A' B' parallel to the 
side A B, either through the other two sides or these 
sides produced. Then the new triangle A' B' C has its 
angles equal to the homologous angles in the original 
triangle ABC. We can now prove that the homologous 
sides are proportional, so that these two triangles are sim- 
ilar (see 65). 

Measure all sides ; divide any one of the original tri- 
angles ABC by its homologous sides in the new triangle 
A' B' C ; the three ratios thus obtained will ail be found 

to be equal, i. e. : — 

AB C A CB 



A! B' CA' C B' 

68. Similar Polygons. — Draw any polygon, A BCD 
E (fig. 7). From any corner, say A, draw diagonals A C, 
A D, etc. Take any point B' in A B. Draw through 
B' a line parallel to side B C in triangle ABC; this line 
will intersect side A C in C, and triangle A B' C will be 
similar to the triangle ABC (67). Through C draw C D', 
parallel to C D, etc. The polygon, A B' C D' E' thus 
obtained will be similar to the original polygon, AB 
C DE. 

In othei I3 ; C D' E' is a drawing to scale ~ 

of the object figure ABODE. 






Lima?* Driving . 3 3 



To confirm by actual measurement, measure all lines 
and calculate the quotients : 
AB' AC AD' 



AB AC AD 

B' C CD' D'E' 



BC CD DE 

You will find all these quotients very nearly equal to 
one another. The more carefully the drawing was done, 
the more nearly equal will be these quotients. 

69. Tou can now draw any simple polygon to scale. 
For example : Make a drawing of a polygon to scale ^. 
The real polygon may be cut out of zinc-sheet or card- 
paper. 

First carefully draw a sketch of the polygon in your 
note-booh ; do this, by free hand, without the aid of a 
ruler, etc. Letter the corners of the sketch (see 8 or any of 
the above figures), and also mark the diagonals of the 
sketch with dotted lines. Then measure all sides and di- 
agonals in centimeters (to first decimal) ; enter these 
figures on the corresponding lines in the sketch, or give a 
catalogue of the same by means of the letters. 

Xow construct one triangle in the real figure after the 
other, according to 60 by taking of each line J for this 
construction. 

If the drawing is to be in any other scale, then the cor- 
responding part of the real lengths must be used (see 66). 

70- The preceding method of dividing the given poly- 
gon into triangles is by diagonals only. But the same 
polygon may be divided in many other manners. For 
example, by one diacjonal and perpendiculars, as shown 
in fig. 8. The drawing to scale is in this case made 
in a like manner. First all the distances, E G-, GH, 
HK, KC on the diagonal, and also the perpendiculars, 
AG, BH, DK, are measured. Thereafter, these lines 
5 



34 Chapter L 



are in succession reproduced to scale on the paper. It is 
evident that in this method the contour lines AB, BU, 
etc., need not be measured in the original. 

A special advantage of this method is its applicability to 
curved lines. This application will become quite evident 
through its generalization in the method of co-ordinates. 

CO-ORDINATES. 

71. If the figure to be drawn to scale contains curved 
lines, or in any other way is more intricate (fig. 9), the 
method of division into triangles becomes impractical, be- 
cause far too many triangles would be required. In such 
cases the method of perpendiculars, just exemplified, is 
used in the following more systematic manner : 

First draw a sketch of the figure in your note-book, as 
represented in fig. 9. Through any convenient point O 
selected in the object draw two lines OX and OY at right 
angles, to each other; enter these lines also in your 
sketch. These lines are called the co-ordinate axes, and O 
the origin of rhe co-ordinates. In the curves, etc., to be 
drawn, mark as many points, A, B, C, etc., as are neces- 
sary to determine them ; especially, also, the points, like 
D, F, K, L, etc, where they intersect the axes, as well as 
the points where two or more of the lines intersect, such 
as points E, M. Always enter the auxiliary lines on your 
sketch. 

From each of these points, such as C for instance, draw 
a perpendicular to the axis OX; such as CQ, from C. 
Then the two Lengths, OQ, cut of from axis OX and CQ, 
the perpendicular belonging to this cut-off piece, complete- 
ly determine the point C. The piece cut off from the 
axis OX, by lie perpendicular, is called the abscissa of 
the point C. ud denoted by x ; the perpendicular itself is 
called the »f the point C, and denoted by y. 

Hence axis OX is called theaxis of abscissas, and 

OT the ordinate oasis. The abscissa and the ordinate of a 
point are called the co-ordinates of a point. 



Linear Drawing. 



35 



In t\\z first quadrant, XOY, the co-ordinates are consid- 
ered as positive ; no sign is prefixed. But in the second 
quadrant, YOX', the abscissa runs from O towards the 
left, while in the first it runs to the rigid to the point 
where the perpendicular intersects the axis of the ab- 
scissas. Hence the abscissa of any point in the second 
quadrant is said to be negative, and marked — . The 
ordinates, like those of H, E, in this second quadrant, are 
drawn from the point dovmwards to reach the axis of the 
abscissas, precisely as in the first quadrant from point C, B, 
etc. Hence the ordinates in the second quadrant are in 
the same direction as in the first, and considered of the 
same sign (-{-). 

In the third quadrant, X'OY\ the perpendiculars from 
any point G have to be drawn upwards to reach the axis 
OX ; hence here the ordinates y are negative. The 
abscissas are here also negative, the same as in the second 
quadrant. 

In the fourth quadrant, XOY, the abscissa are positive 
(+), but the ordinates ar*e negative ( — ). Why ? 

72. For each point to be determined, the co-ordinates 
are measured and recorded in a table in the note book, in 
the following manner: 



POINT, 


CENTIMETERS. 
x. y. 


REMARKS. 


A 
B 
C 
D 
E 
F 
G 


16.2 
12.7 

8.1 
0.0 

— 5.3 

— 7.6 
—10.6 


8.3 
4.6 
6.1 
7.9 
6.2 
0.0 
— 5.7 


Q 

a 
Pi 
< 


H 
E 
K 
L 
M 
N 


— 9.7 

— 5.3 
0.0 

4.2 
13.5 
17.2 


9.4 
6.2 
3.3 

0.0 

— 4.2 

— 6.1 


Q 

a 

S3 

< 


M 

P 


13.5 

19. 4 


— 4.2 
0.0 


Straight Line. 



36 Chapter I. 



In your note book you have now entered on one page 
the full sketch (drawn by free hand, without rulers) with 
all the real lines and the axes drawn out full, but the ordi- 
nates dotted ; on the other page you have tabulated the 
measures taken, as shown above. 

The drawing to scale is now readily obtained by draw- 
ing on paper the two axes and determining each point by 
its abscissa x and ordinate y, agreeable to the scale adopted. 
For example, if the scale be Vio? then the abscissa of the 
point N is, on the drawing, l /io of 17.2 cm. — that is, 1.72 
cm. ; being positive, it is taken from O along the axis of 
abscissas to the right. For the same point 1ST the table 
gives the ordinate — 6.1 ; consequently you draw the per- 
pendicular below the axis OX, and cut off 0.61 cm. or 6.1 
mm. 

73. This method is of very general application. All 
maps are constructed by this method, the abscissas being 
the longitude and the ordinates the latitude of each point. 

The student may practice this method to obtain a drawing 
of the top of a table on which some books, flasks, and other 
apparatus are standing. Use scale 1 / 10 . Take the origin 
O at the left-hand corner of the table, fig. 10 ; the axis 
OX the front edge (to the right) and the ordinate axis OT 
the left-hand ecl^e. In that manner, all on the table will 
be in the first quadrant, so that all co ordinates in this case 
will be positive. 

In practice it is not necessary to give the real co- 
ordinates for each point. For example, the outline of the 
book A B C D on the table (fig. 10) will be determined 
by the full co-ordinates OE, EB of point B ; the additional 
length EF measured, fixes the abscissa OF without meas- 
uring bfcck to (). Then the ordinate FC fixes the point C. 
If now the breadth CD of the hook is measured, its place 
on the table is determined, and can therefore be drawn. 

Accordingly, you can save time by entering these meas- 
ures directly upon your sketch, as shown in fig. 11. Write 



Linear Drawing. 37 



the figures plain, and carefully mark the extremities of the 
length measured, by means of arrow-heads on your sketch, 
as fig. 11 shows. Draw the sketch sufficiently large, and 
as neatly as possible. 

The perpendiculars measured need not be actually 
drawn on the object ; in most cases this would not be per- 
mitted. Simply mark the point of intersection, either by 
chalk, pencil, a pin, a nail, or the corner of a small block. 
For larger figures in the field, these points are marked by 
stakes. 

Further examples : Ground plan of a building, (your 
own school-house, dwelling-house, etc.) or a room (school- 
room), with all the larger fixtures, desks, tables, stoves, 
etc. For these measurements use the meter-rod, and a 
tape made by yourself, of common red tape, on which you 
mark the divisions with ink. Also measure some small 
garden with its divisions, walks, etc. In each instance use 
a scale suitable to the size of the drawing you want to 
obtain. 

Each student should at least make one drawing to scale 
by this method of co-ordinates, from his own measurement 
and sketch of the object. 

74. This method of co-ordinates is very much used in 
physical science to exhibit the simultaneous changes in any 
two variables (compare 42). The one of these variables is 
taken as abscissa, or x ; the other as ordinate, or y. The 
latter (y) is usually considered as the dependent variable, 
while the former (x) represents the independent variable. 
Thus all phenomena changing in time may be represented 
in their magnitude as ordinates y to the time x to which 
they correspond. Here we shall only give a few examples 
for the student's practice. 

In 41 the length 1 and weight w of wires of the same 
thickness and material, have been determined by measur- 
ing and weighing. S"ow draw a line OX> enter on it from 
O the observed lengths 1 as abscissas x, and erect perpen- 



58 Chapter I. 



dicularson which you cut off ord mates y, so as to represent 
the weight observed according to any convenient scale ; 
for example, one gramme to the centimeter". 

The points thus determined represent exactly your ob- 
vations. You will find that they are all nearly in a 
straight line passing through O. Hence the relation be- 
tween weight and length of uniform wire is expressed by a 
straight line, if the length is taken as ordinate, the weight 
as abscissa. 

So also you may take the homologous side in the similar 
polygons of 46 as abscissa on the same diagram, and the 
corresponding weight as ordinates. The points thus 
determined in your w T ork done in 46 will determine a 
curve. Draw the same so as to pass as near all the points 
as possible for a continuous curve. This curve according- 
ly expresses the relation between weight and dimension of 
similar polygons cut out from any uniform material. 

The same construction may be performed for the 
volumes and dimensions observed in 47. 

In all cases adopt any convenient scale for the depend- 
ent variable, such as 1 gramme to 1 cm., Ice. to 1 
cm, etc. 

Such graphical representations of the simultaneous vari- 
ations of two quantities are very useful in many branches 
of physical science ; they show the relative changes in 
magnitude much better than the columns of figures ob- 
tained by direct experiment or observation. 

PROJECTIONS. ' 

75- A drawing of any body, so constructed, that the 
drawing appears to an eye, placed in a proper position, 
exactly as the body itself, is called ^projection of the body. 

A horizontal projection shows how the body appears on 

♦That is, 7.4 gr. would be represented by an ordinate 7.4 cm. long. 



Linear Drawing, . 39 



a horizontal plane to an eve placed very far* above the 
body. A vertical projection exhibits the body seen against 
a vertical plane by an eye placed very far in front of the 
body. 

On most bodies, both vertical and horizontal planes are 
quite frequent. But in a horizontal projection, all vertical 
planes will necessarily appear merely as lines, and cannot 
be recognized as planes in their true shape. So also all 
horizontal planes appear as lines in a vertical projection. 
For example, a cube will, in a vertical projection, appear 
merely as a rectangle, and in the horiz«:»nal projection 
square only. 

Hence, for practical reasons, some oblique pr 
should be used for actual bodies, representing then 
from, a point far above and to the right of the body againsr 
a plane at right angles to this line of sight. It is found 
that such a projection can be constructed by means of the 
three dimensions of the bodie- as measured along tl 
co-ordinate axis. Hence this mode of projection is also 
called OQBOfl The' following is the 

simplest method of this kind, and of great use to students. 

76. Axonometric Dbawixg-. — Bepresent all vertical 
lines by vertical lines, and to full scale ; all horizontal 
lines running right and left also horizontal and to full 
scale : but all horizontal lines at right angles to the latter 
put down to one-half scale, and inclined half a right angle 
to both the vertical and horizontal. 

This simple rule is exemplified in fig, 12. which repre- 
sents a rectangular block to scale J, having the sides AB 
10 cm., BD S cm., and BC 6 cm. in reality, Hence in 
the drawing we have the- vertical BC, vertical and full 
scale (i of 6 cm. > or 1.5 cm. : also the horizontal AB is 



the lines from the dineren: parrs of the body to the eye are 
parallel to each other. 



40 Chapter I. 

full scale [^ of 10 cm.), hence 2.5 cm. long and horizontal ; 
but !>i) is inclined equally toward BC and BA, and only 
7 , that is, -£ of J, or -^ of 8 cm., or 1 cm. long. 

77. For practice, construct from rectangular wooden 
blocks ot proper sizes, any convenient form (see fig. 13), 
and make an axonometric drawing thereof to scale. 

To do this, place yourself in front and to the right of the 
object thus built up. Draw, by free hand and without 
rulers, a rather large sketch in your note-book, represent- 
ing the object as nearly as possible. 

Measure (in cm.) all necessary dimensions of the object, 
and enter the result along the corresponding lines in the 
sketch. If any doubt can arise in regard to the points 
from which the given measure was taken, put arrow- 
heads on the extremity on either side of the measured 
line. This is shown in fig. 13, but on a scale much smaller 
than practicable for the student. 

From the sketch thus obtained the drawing is made 
to scale, and accurately, on smooth, w r hite paper, by 
following the rules laid down in 76. Figure 13 is drawn 
to scale x / 10 . 

The student should, by all means, practice this art. Let 
him first select simple objects accessible to him ; let him 
draw the sketch, measure, and enter the measurements on 
the sketch. Then carefully make the drawing in -£, J, 
*/ 5 , x / 10 , or any scale convenient (size of paper and magni- 
tude of object determine the scale). This is a most inter- 
ttg and profitable exercise. 

78. In the drawing, merely dot those lines wdiich in 
the object could not be seen when observing the latter as 
directed in 77. All other lines may be drawn out in 
full. 

7, the beginner had better not meddle with. 

79. This method of drawing is much used by engi- 
neers, architects, carpenters, etc. It is also used for repre- 



Linear Drawing. 41 



senting, correctly and to scale, the different chemical and 
philosophical apparatus. Hence the great importance of 
this art to the general student; for, without becoming 
familiar with these methods by actual practice, the 6tudent 
will remain unable to understand the figures of apparatus 
given in the books. 

The artisan performs the inverse operation. Given the 
object, the student prepares the accurate drawing thereof. 
Now, given the accurate drawing to scale, the artisan is 
able to construct the object ; for the actual length of any 
part is easily obtained by measuring its projection on the 
drawing and dividing by the scale used. 

80. From the preceding it is evident that axonometric 
drawing essentially consists in the application of co- 
ordinates to the three dimensions of space (compare 1 
and 71). It is customary to denote the vertical axis, as 
in figure 11 by OZ, the horizontal to the right, OX, and 
the horizontal fronting the observer by OT. Of course 
all three axes are extended beyond the origin, thus giving 
rise to negative axes and co-ordinates. 

Any point M in space now is fully determined by its 
three co-ordinates ; by 

Z==MJST, the distance of M above the plane XOT, 
measured in the direction OZ ; 

y=N!Sr, the distance of the perpendicular MN from 
plane XOZ, and measured along axis OY ; and 

x^OJN 7 , along axis OX. — 

The co-ordinates are usually given in the order x, y, z. 

The student may determine the co-ordinates of a few 
points in the room, by taking the origin in one of the 
corners at the floor of a room, and the axis along the 
three edges of the room which meet in that point. 
6 



CHAPTER II. 



MECHANICAL WORK AND MACHINES. 



81. A Machine is a contrivance for the transmission 
of force. Thus a wagon is a machine, because it transmits 
the force of the horses to the, burden on the wagon. 

The force applied is called the power, P; the contriv- 
ance from which the force is obtained is called the motor. 
Thus, the horse drawing a cart is a motor ; the actual pull 
it exerts at any time is the power. 

The force overcome by the transmission of the power is 
called the resistance, R. The friction of the wheels of the 
cart against the axles and the ground constitute the resist- 
ance in the case here alluded to. 

The term force itself is used to denote that which pro- 
duces changes or resists motion. In its broadest sense, 
force, therefore, is motion. 

82- A force will be completely determined by its 
point of application, direction and intensity. 

The point where the force exerts its action is the point 
of application of the force. The direction of a force is the 
line, drawn from the point of application, along which the 
force acts. The intensity of the force is the number of 
grammes, or kilogrammes, which equal the same. If the 
direction of the force be vertically downwards, its intensity 
can be easily determined by simply replacing the force by 
a sufficient number of grammes. If the force has any 
other direction, its intensity can be determined by the 
dynamometer. 

83. A common spring-balance forms the simplest 
dynamometer. The scale of the spring-balance is deter- 
mined by suspending known weights to the same and 
marking the position of the tongue on the scale. If, then, 



Mechanical Work. 43 



by any other force the tongue is brought to this mark, the 
force is evidently of the. same intensity as the number of 
grammes marked on the scale. 

In this manner, the intensity of the pull of horses, etc., 
is ascertained. 

84. The mechanical work, W, of any force, F, is meas- 
ured by the product of the force, F, into the distance, D, 
through which the force is actually exerted. 

A force of one kilogramme exerted through one meter 
is called a kilogramme-meter (abbrev. kgm). A force of 
two kilogrammes exerted through one meter represents 
evidently twice the above work ; so, also, one kilogramme 
exerted through two meters ; but two kilogramme-meters 
is the product in each case. So in all other cases. In- 
stead of the kgm. the gramme-meter (gm.) is also used as 
unit of work. 

In general, the unit of mechanical work is the exertion 
of a unit of force through a unit of distance / it may be 
called a dynamo. Thus, if the kilogramme is the unit of 
force, and the meter the unit of distance, the dynamo is 
a kilogramme-meter. So, also, in all other cases. 

For example : The work done by a horse in a horse- 
power machine each second is a pull of 45 kilogrammes 
exerted through 0.9 meters ; that is, 0.9.45=40.5 kilo- 
gramme-meters. The work of an ox per second is a pull 
of 60 kilogrammes exerted through 0.0 meters, or 0.6. 
60=36.0 kilogramme-meters. Hence, the mechanical 
work of an ox is only 9 / 10 of that of a horse when used in 
a, horse-power (machine). 

85- When a horse acts to its very best advantage, it 
can, during a short time, accomplish a mechanical work 
of 75 kilogramme-meters per second / this amount of 
work has therefore been generally accepted as a standard 
of steam horse-power. 



44 Chapter II. 



In the horse-power machine a horse accomplishes, 
according to the preceding, only 0.53 horse-power, and an 
ox only 0.48 horse-power. In the same machine a man 
exerts a pull of 12 kilogrammes through 0.63 meters, or 
accomplishes 12.0.63=7.56 kilogramme-meters a second ; 
hence does l / 10 of a horse-power. 

86. The amount of mechanical work which a man can 
produce in one day depends very much upon the circum- 
stances under which he has to work. Evidently, the 
greater the mechanical work necessary to move his own 
body during the labor, the less will be the amount of 
mechanical work accomplished by the man. 

It has been found that a man, in raising water, can 
accomplish the following mechanical work per day (in 
kilogramme-meters) : — 

With a light bucket, 92,000; with a light shovel, 
96,000 ; with bucket and rope over pulley, 154,000 ; by 
means of an Archimedes screw (inclined under 30° to 40° 
to the horizon, and containing three tubes rising 20° to 
23° against the tangent), 90,000. In the first two cases 
the man has to move his own body much more than in the 
last two cases ; hence the striking difference in the amount 
of (external) work accomplished. 

87. The power, P, applied to a machine is exerted 
through a certain space, p, each second of time ; hence, 
the mechanical work applied to the machine is — 

P.p Dynamos. 

When the machine is in motion, the space, p, can easily 
be measured ; the power, P, is also measured by a dyna- 
mometer, or otherwise. Thus, the work applied becomes 
known. 

The resistance, R, overcome by the machine, moves 
each second through a certain space, r, which also can be 
measured directly. Hence the mechanical work done by 
the machine is — 

R.r Dynamos. 

Since this is mostly outside the machine, the work done 
is also termed the external work. 



Machines. 45 



But the machine consists of many parts which, during 
the working of the machine, have to move upon one 
another. Thus mechanical work is performed in the 
machine also; this work is termed the internal work, and 
may be denoted by I. 

It is evident that a machine cannot create mechanical 
work / hence all the work done or expended by a ma- 
chine, both internally and externally, is due to the work 
applied by the power. Therefore we have, for all ma- 
chines, without exception, the following general law: — 

P.p=R.r+I. 
That is : fThe work applied by the power is equal to the 
work overcome in the resistance, plus the internal work 
required to move the parts of the machine itself. 

88. The external work done by the machine, E.r is 
produced by the expenditure of P.p ; hence the fraction, — 

K.r 

represents the proportion of useful effect yielded by the 
machine. The scientific machinist tries, therefore, to re- 
duce the internal work, I, the utmost ; for, as I dimin- 
ishes, the external work increases, until for 1=0, c be- 
comes equal to unity, so that the entire work applied is 
transmitted to the resistance. We need, however, hardly 
add the statement, that there is not any machine for 
which the internal work, I, is zero; in most cases the 
amount of internal work is quite large. 

89. It is, however, necessary to study the simple ma- 
chines first under supposition that the internal work is so 
small that it may be neglected. We shall then have — 

P.p=R.r orP=-^K 
for such machines. 

The simple machines, of which all complex machines are 
composed, are often termed the mechanical powers. They 
are : the pulley, the inclined plane, and the lever. 



46 Chapter II. 



90- The pulley is a wheel free to turn on its axis, and 
having a groove to receive a cord. The pulley is said 
to be fired or movable, according as the axis is either 
fixed or movable. 

Experiment with pulleys made of brass, and provided 
with very flexible cords. To diminish the friction (inter- 
nal work) as much as possible, oil the axis. As weights, 
use small tin buckets and shot; it is convenient to have 
these buckets marked P and R. Use a much smaller size 
of shot* for P than for R. Determine the actual weight 
by weighing the buckets with their contents. For each 
pulley make a series of experiments ; for each new experi- 
ment adding a few more large shot into bucket R, and then 
restoring equilibrium by adding enough small shot to bucket 
P. Record the experiments in the note-book in columns : 
1st, number of experiment; 2d, weight of resistance, R; 
3d, weight of power, P, observed; 4th, calculated value, 
P^-.=R (see 89) ; 5th, difference, d, between the observed 
P and the calculated P; this difference is evidently the 
measure of the internal resistances. Each such table for 
any given system of pulleys is to be headed by the value 
of the fraction y, which you first of all ascertain by direct 
measurement. 

91. In this manner you will find : — 

1. For the fixed pulley the power is equal to the resist- 
ance, P=R. 

2. For a single movable pulley, the power is one-half the 
resistance, P=\ R. 

Similar results obtained for combinations of pulleys. 

The wheel and axle, the windlass and capstan, are com- 
binations of the pulley with the lever, and therefore not 
simple machines or mechanical powers. • 

92. A plane, forming an angle with the horizon, is 
called an inclined plane. The angle thus formed is called 



♦The numbers BBB and 2 will answer. 



Machines. 47 



the inclination of the plane. Hence, if the inclination is 
zero, the plane is horizontal ; if it be 90°, the plane is 
vertical. See fig. 15. 

The weight of the body (wagon) on the inclined plane 
acts vertically downwards ; it is the resistance, JR. In 
order to retain the body at rest on the plane, a power, P, 
must be applied to the body in some direction. We shall 
here consider only the one case, where this direction is 
parallel to the inclined plane. This is secured by attach- 
ing a pulley, C, to the top end of the board, AB, serving 
as inclined plane, and passing the cord attached to the 
wagon, W, over the same to the power, P. Here a like 
pair of buckets for shot may be used. The weight of the 
wagon must, of course, be added to that of the bucket ; or, 
simply nail the bucket to the wagon, and weigh the 
whole as one. In order that I may be nearly nothing, the 
wagon must run on good wheels and rail-wires. (See 87.) 

Note the result of experiments as before. First, find, 
by measurement, the fraction ^- Be careful to observe, 
that p is the motion along the plane, or the sinking of the 
power, P, while r is the distance through which E is over- 
come (or exerted) ; that is a vertical distance, since R is a 
weight, and therefore acts vertically downwards. From 
this it is readily seen, that the fraction 

r height of plane, DB h 

p length of plane AB 1 
In the first column give the number of your experiment. 
In the second, the weight, R; in the third, the observed, 
P ; in the fourth, the calculated, P= r /p R= h /i R ; in the 
fifth, the difference, d, between P observed, and P= h /i R 
calculated. This difference expresses the internal resist- 
ances and errors. 



93. Consequently, by 89, — 



r h 

P 1 

or P : R = h : 1 



48 Chapter II 



That is, on an inclined plane, and "for the power par- 
allel to this plane, a weight, R is in equilibrium, if the 
power, P, is to the resistance, R, as the height, h, to the 
length, I, of the plane. 

If the inclination of the plane can be changed, you can 
repeat the whole series of experiments for several different 
inclinations or different values tff h /i . 

The screw is an inclined plane wound around a cylin- 
der; hence, not a simple machine. 

94. The lever is an inflexible bar, exactly balanced on 
a horizontal axis, which is called the fulcrum.* Fig. 16. 

Weights may be suspended on either side of the ful- 
crum and moved to and fro until the lever is again bal- 
anced, or in equilibrium. This is best observed by having 
a pointer or tongue, t, attached to the lower middle of the 
lever. It is best to first only suspend one weight on each 
side ; for example : a tin bucket more or less filled with 
shot. The lever may be provided with an accurate milli- 
meter scale, counting on each side from the fulcrum, as 
zero. This distance, from the fulcrum to the weight, is 
called the lever-arm of the weight. We shall denote the 
lever-arm of the power, P, by p' ; the lever-arm of the 
resistance, R, by r'. 

It is very easily seen — or ascertained by direct measure- 
ment — that the distances moved over by resistance and 
power are proportional to the corresponding lever-arms ; 
that is, — 

r r' 

This can also be ascertained by means of a simple con- 
struction on paper. 



*A beam of wood, about 50 to 100 cm. long, 1 cm. wide, and 2 to 3 cm. high, sus- 
pended by a thin, iron wire hoop, passing through the top corner of a triangular 
hole, will answer well enough. 



Machines. 49 



95. According to 89, we have, for the lever, as 
machine, — 

r 
P = — . E 

P . (1) 

Therefore, by the above value of this fraction, — 

r' 
P = — . E 

P' (2) 

which, by division with E, becomes — 

P r' 

E = 7 (3) 

but by multiplication with p' (2) becomes — 

Pp'=Er' (4) 

The law of the lever is expressed by either of these 
equations. Translated into words (3), reads: The power- 
P, is to the resistance, R, inversely as the lever-arms 
(r s top'). In the equation (4) occurs the product of a force 
into its lever-arm. This product is termed the momentum 
of the force. Hence (4) reads : — 

The momentum* of the jjower, P, is equal to the mo- 
mentum of the resistance, R, if the lever is in equilibrium. 

This latter expression of the law of the lever is evi- 
dently the simpler of the two. 

But the above law has only been obtained from the 
general equation, 89, expressing the equilibrium of all 
machines ; it, therefore, has yet to be demonstrated by ex- 
periment, for the lever. To experiment, fill some shot 
into the buckets, P and E; weigh these buckets, thus 
determine the ratio p /r. Then suspend E to the lever at 
an arm r', and slide P until the beam is level ; then read 
off the corresponding lever-arm, p'. Next calculate the 
ratio, r '/ P '. Finally subtract this from the ratio, F / R of the 
forces ; this difference, d, is due to the internal resistances 
of the lever, and will always be found to be small. 

^Momentum is the product of the force into its lever-arm. 



50 



Chapter II. 



Change r', the arm of R, several — at least 10 — times, 
and for each new position produce equilibrium by moving 
P. 
Arrange the result in your note-book, thus : 
Series I. P= R = - P / R — •••■ 



Exp. 



ltolO 
or more. 



r 
r' p' — d 
P^ 



hence Momenta 



Pp' 



Rr' 



Work several series. Calculate the momenta, Pp', and 
Rr'. 

You will always find the difference between the ratio 
of the forces and the inverse ratio of the lever- arms 
very small, provided the internal resistances be small. 
The momentum, Pp', of the power, will be found very 
nearly equal to the momentum, Rr', of the resistance. 

96- The center of gravity of any body can be determined 
by an application of the law of the lever ; for the center 
of gravity is the fulcrum-point, about which all the parts 
of the body itself exactly balance one another. The 
center of gravity can therefore also very readily be found 
by direct experiment. 

97- By the preceding experiments the general law — 
87-89 — has been demonstrated to be a fact, for the 
three simple machines, or mechanical powers ; at least, in 
case the internal resistances are small, or nearly zero. 

Since all machines are composed of these three mechan- 
ical powers, the same law must be true for machines in 
general. 

But it has, during the last forty years, also been 
proved to be true for all phenomena in nature ; so that 
amid all the vicissitudes of nature, the total amount of 
mechanical work remains forever the same. This princi- 
ple is known as that of the correlation and conservation 
of forces. 



Machines. 51 



98- If an y weight, W kilogrammes is to be lifted 
through a height, h meters, it requires an expenditure of 
mechanical work of W.h kilogramme-meters (see 84) ; 
for throughout the entire vertical distance, h, the entire 
weight, W, has to be overcome. 

But it is immaterial in what way the weight is lifted ; 
whether in a vertical, or along any other path, provided 
the entire change in level he the same. If, however, the 
lifting is done by means of machinery, the internal work 
will, of course, depend upon the manner in which the 
weight is lifted. 

99. If now the body of weight W* kilogrammes in 
any manner, is again brought down through a vertical 
distance of h meters to its original level, it will necessa- 
rily expend the same amount of mechanical work which 
was required to lift it. 

If the body falls freely, hardly any of this work, W.h, 
is consumed by internal work ; for the resistance of the 
air is not considerable. If, however, the body rolls down - 
an inclined plane, a greater or less portion of the power 
will be consumed by friction, so that the mechanical work 
which the falling body can do will be less than W.h. 

100. Water flowing in tubes, or canals and rivers, is 
used to perform mechanical work in factories by placing 
proper motors in the water's course. Such motors are 
Water-wheels and Turbines. 

If W kilogrammes (or cubic decimeters) of water 
flow per second down h meter, the mechanical power 
of this water-course will be w - h /75 horse-powers (85.) If the 
water flows in open canals, some of this power is con- 
sumed by friction against the walls of the canal; if the 
water flows through tubes, this internal work, to be de- 
ducted from the above, is greater still. 

How the mechanical power of water can be calculated 
from the velocity and quantity of the water, will be shown 
in the subsequent. 



52 Chapter II 



101. Of all the internal resistances in machines, fric- 
tion is the most common. Friction is due to the rough- 
ness of the surfaces sliding over each other.* 

By means of the Tribometer ' (fig. 17) the laws of sliding 
friction can be experimentally deduced. In its simplest 
form, the tribometer consists of a plank, AB (2 to 3 meters 
long, 2 dm. wide, 4 to 6 cm. thick), supported horizon- 
tally. Over a pulley, 0, at one £nd of this plank, passes a 
flexible cord, DCE, one end of which is attached to the 
sleigh, S, on the plank, while to the other end is suspend- 
ed a tin bucket, P, for the reception of the power. The 
plankf must be above the floor at least 2 meters, or it 
must be placed near a hole in the floor, so that the bucket, 
P, can sink through the floor into the story below. By 
proper supports, the bucket is stopped, in its descent, a 
little before the sleigh reaches the end of the plank. The 
sleigh may consist of a simple piece of wood (1 dm. wide 
and more or less long) ; or it may be provided with run- 
ners of different length and breadth, and of different ma- 
terials (such as wood, metal, etc). Finally, a wood — or 
tin — box is placed on the sleigh, to receive the burden, 
R producing the resistance. It is most convenient to cut 
a number of 100 and 50 gramme pieces from common lead 
bars, and use these to weigh down the sleigh, while the 
bucket is filled with the proper amount of shot. 

The sleigh is started by a gentle blow. If it continues 
to move uniformly, the power, P, is just enough to over- 
come the friction, F, produced by the weight R. If the 
sleigh stops, more shot has to be added to the bucket; 
if it moves with increasing rapidity, shot have to be taken 

♦Under a magnifying glass, or a microscope, even the finest-polished surface 
looks rough. The edge of a razor looks like a saw. 

fTf its supports are one meter high, and the whole is standing on a table, a 
sufficient height is secured above the floor. 



Machines. 53 



out from the bucket P, or more weights must be added to 
the bucket B. 

The experiments are recorded in the note-book in the 
following manner : — 

1st. Describe the kind of sleigh used ; whether wood, 
what kind, how the grain runs, etc. 

2d. Perform a series of experiments made with increas- 
ing E. Give, in first column, the number of the experi- 
ment ; in the second, the total weight, E, of sleigh, box 
and weights ; in the third column, the weight, P, of the 
bucket, with shot sufficient to move the sleigh' uniformly ; 
in the fourth column, give the ratio p /r= £ 

102. You will find this ratio practically constant for 
each series of experiments ; that is, the friction, P, is 
proportional to the pressure, JR. 

P=f. E. 

The value f. is called the co-efficient of friction. 

By making several series with different sleighs, you will 
find that this co-efficient is independent of the extent of ur- 
f ace in contact (and of the velocity). Ton will then, also, 
find the value of f for the different materials ; viz : 



Dry. Tallow. 



Wood upon wood 0.36 

" " metals 0.42 

Metals " " 0.18 



0.07 
0.08 
0.07 (oil) 

Lubricants, such as tallow, soapj oil, very much dimin- 
ish friction. The above co-efficient has been found for 
surfaces very thinly coated with tallow, as given in the 
second column of figures. To verify the last values, a 
thin board, coated with the lubricant is put upon the tri- 
bometer plank, and separate lubricated sleighs are used, 
also. 

By means of the dynanometer and a small, two- wheeled 
cart, loaded with stones, etc., the student can easily ascer- 
tain the co-efficient for common roads. The greater the 



54 Chapter II 



radius of the wheel, the smaller the coefficient. On 
macadamized roads, the co-efiicient for wagons varies from 
V30 t° 78o> while on dry earth road it varies from x /3o to 
x j b0 . In a sandy or muddy road, the co-efficient increases 
to 1 / l0 or more ; while on railroads the co-efficient is only 
Vsoo to 1 / 150 , according to the velocity of the train. By 
means of these values you can solve many problems. 
Thus, a locomotive and tender weighing 40 tons (40,000 
kilogrammes), require, by slow velocities (12 miles an 
hour), on a horizontal railway, a power of 40O00 / 300 ==133 
kilogrammes, while a fast train (50 miles an hour) a trac- 
tion of 4O000 /iM === %66 kilogrammes would be required. 

The co-efficient of friction of flat, steel skates, on ice, 
was, by Mueller, found to be from 0.02 to 0.03. 

By means of these figures, many problems of practical 
engineering can readily be solved. 

103. Composition and Resolution of Forces. — Two 
forces, P and Q, having the same point of application and 
the same direction, evidently produce an effect equal to a 
force R, applied at the same point and in the same direc- 
tion, but having an intensity equal to the sum of the 
intensities of the given forces, P and Q. That is, 
R=P+Q. 

Accordingly, the one force, R, is equivalent to the two 

forces, P and Q. These latter are therefore called the 

Components, while R is termed the Resultant. [Define 
these two terms.] 

104. If, however, the two forces, P and Q, having the 
same point of application, possess opposite directions, then 
their resultant, R, will evidently be equal in intensity to 
their difference, P — Q, acting in the direction of the 
greater force, P>Q. That is, R=P— Q. 

Finally, if in the latter case, the two opposite forces are 
equal, P=Q, the resultant will be zero, R=0. This is 
also self-evident. 



Machines. 55 



105. A force R', equal and opposite the resultant, R, of 
two forces, P and Q, will balance these latter (fig. 18). 
For R and R' balance each other (104), but R is equiva- 
lent to P and Q (103), hence, R' balances P and Q. 

These propositions (103-105) are all self-evident, and 
much used in common life. They are also easily experi- 
mentally demonstrated by means of pulleys and weights. 
We shall not do this, because we have already applied all 
these propositions in the preceding experiments. Here it 
was essential, however, to accurately and concisely state 
these propositions. 

106. Two forces, P and Q, fig. 19, having the same 
point of application, A, but including an angle (P, Q,) be- 
tween themselves, are equivalent to a resultant, R, acting 
at the same point, A, and determined in direction and 
intensity by the following, so-called, law of the parallelo- 
gram of forces. 

Represent the'given forces, P and Q, acting on A by 
straight lines, AB=P and AC=Q, including between 
them the given angle (P, Q)=BAC, between the forces, 
and represent the intensity of the forces, P and Q, by the 
length of these lines according to any convenient scale.* 
Then complete the parallelogram by drawing a line 
through B parallel to Q=AC, and a line through C paral- 
lel to P=AB. The point of intersection of these two 
lines, mark D; draw the diagonal, AD, from the point of 
application, A. Then this diagonal, AD, will, in direction 
and length, represent the direction and intensity of the 
resultant, R, of the two given forces, P and Q. 

By producing DA backwards, beyond A to D', making 
AD'=AD, the line AD, will, in the same manner, repre- 
sent a force, R', equal and opposite to the resultant, R. 
Hence the three forces, R', P and, Q, will balance. 
(See 105.) 

*F. Ex. each gramme by a centimeter ; thus if P=20 grammes, th« line AB i* 
made 20 centimeters long. See 75. 



56 Chapter II 



This is the complete statement of the law of the paral- 
lelogram of forces. We shall now demonstrate the same 
by experiment. 

107- A vertical wooden frame, fig. 19, about one 
meter square, has, near each extremity of the upper beam, 
a pulley pending downwards. A flexible cord passes over 
these pulleys. By buckets with shot (or weights), the 
weights P and Q, are attached to the extremities of the 
cord, while a weight, R', is suspended (by a shorter cord 
tied to the longer one) somewhere between the two 
pulleys. 

If R' is greater than the difference between P and Q, 
but less than their sum, the cord will, after a few oscilla- 
tions, come to rest; if R' is pushed up, it will sink down 
again as soon as you slip the same, provided the pulleys 
move with but very slight friction. Accordingly, P, Q, 
R' mutually balance one another. 

108- Now measure the angle included between P and 
Q, that is (P, Q) ; also the angles (P, R') and (Q, R'). 
Measure these angles by holding the card goniometer (36) 
in front of the cords. Copy these angles accurately on 
paper, or measure them in degrees by means of a pro- 
tractor.* 

If buckets with shot were used as weights, then weigh 
these buckets with contents. Register your observations 
in columns, giving in the first column the number of your 
experiment; in the second, the value of P; the third, 
the value of Q; the fourth, the value of R' ; the fifth, 
the value of (P, Q)=BAC ; the sixth, the value of 
(P, R')=BAD' ; the seventh, the value of (Q, R')=CAD'. 

109. Then, on paper, accurately lay off a straight line, 
D'A, to represent R', according to any convenient scale.* 

lente will find it easier to hold a piece of card-board — or white paper 
, ill board— vertical and clone behind the cords running from A 
<fi_r. l tie point A. and one point exactly back of each of 

the cord- AP>. AC. and Al>' with pencil, on this card, at reasonable distances from A. 
Then rake down the card, and join these three points with A, and you will have the 
true magnitude of the three angles, which you now can measure by means of the 
ho;n protractor (see 86). 



Machines. 57 



Prolong D'A to D by making DA=AD'. With a radius 
equal to Q, describe an arc of a circle from D to the right 
•of AD, and from A to the left of AD. With radius 
equal to P, describe an arc of a circle from D to the 
left of AD, and from A to the right of AD. The point 
of intersection to the right of AD, mark B, that to the 
left of AD, mark C. Then draw AB and CD, also AC 
and DB, which, if the drawing was accurately done, will 
be parallel two and two. Finally, mark AD by R, AC by 
Q, AB by P, and AD' by R'. Now measure the angles 
(P, Q) and (P, R v ) and (Q, R) on this drawing, by means 
of a protractor ; enter these values in an eighth, ninth, 
and tenth column in the note-book as calculated (or con- 
structed) values. 

You will find that these values are very nearly the same 
as those directly observed on the apparatus with the 
weights. Hence the law of the parallelogram of forces 
is a fact. If the friction of the pulleys be sufficiently 
small, and the work done with proper care, the observed 
and calculated values are practically equal. 

This great law has been confirmed by all researches on 
the action of forces. 

110- According to the proposition demonstrated in the 
preceding, two forces, P and Q, acting upon a point, A, 
can always be replaced by one force, R, equivalent there- 
to. This constitutes the composition of forces, which, of 
course, may be extended to 3, 4, or any number of forces 
acting upon one point. 

Hence, it follows that any one force, R, may again be 
resolved into two (or more) forces, P and Q, provided only 
these latter form the sides of a parallelogram, of which R 
is the diagonal passing through their common point of ap- 
plication. This process is termed the resolution of forces / 
it is of the greatest importance in physical science. 

*Mark the scale used on your drawing. You will find it most convenient to 
take 1 gramme to the centimeter; at times, however, you must take 2 or more 
grammes to the centimeter, in order that the drawing can find room on the paper. 



58 Chapter II 



A great many problems can readily be solved by means 
of this theory of the composition and resolution of forces, 
expressed in the parallelogram of forces. Thus, if the. 
action of any given force, R, fig. 20, in any given direc- 
tion, AB, is to be determined ,draw a perpendicular, CD, 
from the extremity, C, of R, to the given direction ; the 
piece, AD, cut off, represents the component sought. The 
inclined plane is a special case of this kind. 

By means of these laws, many problems occurring in 
practice can readily be solved, either by geometrical con- 
struction, or by simple calculation. Examples will be 
given in another place. 



CHAPTER III. 



MOLECULAR PROPERTIES OF MATTER. 



I. Solids, Liquids, and Gases. 

HI. All bodies consist of parts. Thus, a cubic deci- 
meter, or liter, contains 1,000 cubic centimeters (see 9), 
and one cubic centimeter contains 1,000 cubic millimeters, 
so that in a body of one liter there are one million of parts, 
each of one cubic millimeter in size. But each such part 
— being much larger than a common pin-head or a 
grain of sand — may again be divided into smaller parts, 
or particles. 

Yery small parts of a body are termed the molecules 
of the body. A body is, therefore, simply the sum of its 
molecules; the properties of the bodies are, hence, pecu- 
liar to the molecules of the same, and termed molecular 
properties. 

112.* A piece of steel, iron, lead, or a glass-rod and 
a stick of wood retain their form with considerable 
power. Their particles are not readily "moved amongst 
themselves / for these bodies resist the blade of a knife or 
the point of a needle with more or less force. They are 
termed solid bodies. 

But water yields most readily to knife-blade and 
needle ; that is, the particles of water readily move or 
flow aside to give place to the solids. Bodies, the parti- 
cles of which move very readily amongst each other, are 

*The student must, of course, actually make all the observations here men- 
tioned. He must, therefore, be furnished with small pieces of the solids ; also 
small bottles filled with the different liquids, and a beaker-glass containing water. 



60 Chapter III. 



termed f»hl$. The same is observed when water is 
poured from one vessel into another. 

Accordingly, air is also a fluid; for we move ourselves 
with ease in and through the air. But while water does 
not perceptibly change its volume under pressure, air does 
change its volume very much when pressed. 

Hence there are two kinds of fluids, namely, compress- 
ible and incompressible fluids. The first are called gases, 
the latter are termed liquids. 

From the above we derive the following classification 
of bodies. 

iNot readily movable Solids. 
Readily movable ; j Not compressible . liquids 
Fluids. \ Compressible Gases. 

113. Water, when exposed to great cold — as during 
the winter — becomes solid, and then is termed ice. 
By putting a small test-tube full of water into a freezing 
mixture,* the water is easily frozen, or converted into 
solid ice, at any season of the year. 

If the water contained in a small porcelain dish is 
heated over an alcohol lamp, the water soon disappears, 
apparently; it has been converted into steam, which is 
not distinguished in the air because it has the same 
color as the air. We shall afterwards learn, with greater 
certainty, that steam is water in gaseous condition. 

Hence water is, according to circumstances, either a 
solid, a liquid, or a gas. Therefore the above classifica- 
tion (72) is not absolute ; but only relative. Instead of 
speaking of three kinds of bodies, we must therefore only 
speak of matter, as in three conditions — the solid, liquid 
and gaseous. These three conditions are also termed the 
three states of aggregation of matter. 

About a decigramme of Iodine put in a test-tube closed 
by fusion, is most admirable for the exhibition of these 

♦The most common freezing mixture is obtained by mixing two parts of 
pounded ice with one part Of common salt. 



Matter. 61 



three states. The solid, black iodine fuses readily when 
the tube is held at some distance above the alcohol flame ; 
you can, by properly inclining the tube, see the liquid 
iodine flow down the walls of the glass. At the same 
time the tube becomes filled up with beautiful violet va- 
pors of iodine, or iodine gas. If you put the tube away 
from the flame, the vapor will condense to beautiful black 
crystals of solid iodine again. This experiment may be 
repeated at pleasure with this apparatus. 

114- But the mobility and compressibility of the par- 
ticles of bodies are of all degrees, so that no rigid classifi- 
cation is possible. Thus lead and steel are solids ; but by 
the sharp point of the knife you will easily find that the 
particles of lead are much more easily moved amongst one 
another than those of steel ; in other words, steel is more 
solid than lead, or lead is more fluid than steel. Accord- 
ingly, lead can be pressed into tubes, the solid lead 
actually flowing out of the molds under high pressure; 
but even steel, when very hot and violently beaten with 
heavy hammers, is sufficiently fluid to be forged, whereby 
the particles move amongst one another, as in liquids. 

Many solids have a much less degree of solidity than 
lead ; such are bees-wax, butter, etc. On hot summer 
days such bodies become almost as liquid as the liquid tar 
is in winter. 

The degree of mobility in the particles of a liquid is 
termed limpidity y while the viscosity of a liquid ex- 
presses the resistance to motion among the particles. 
Thus tar has a high degree of viscosity; syrup has less 
viscosity, glycerine still less, and water is, in common life, 
no longer considered to have any viscosity, but to be 
limpid. Alcohol, ether, gasolene, and like liquids, have, 
however, a higher degree of limpidity. Observe these 
degrees of mobility yourself, by shaking the bottles con- 
taining the above-named liquids. You may, at the same 
time, notice the odor peculiar to many of these liquids, so 



62 Chapter III 



that you may readily recognize them, even without read- 
ing the labels on the bottles. * 

Finally, it should be stated, that the fluids also differ 
much in compressibility, and pass through regular grada- 
tions from liquids, through vapors, to gases. Nowhere can 
a sharp line of separation between these states of aggre- 
gation be drawn. 

115. Water is the most common liquid. We may 
therefore study it as representing the whole class of 
substances in the liquid state. So, also, common atmos- 
pheric air is studied as representing any gas. After 
having studied these flu-ids, we shall be prepared to study 
the more varied molecular properties of solids. 

II. MOLECULAR PROPERTIES OF LIQUIDS. 

116. The free surface of any liquid, is plane and 
horizontal, or level. 

To ascertain this fact, use the plumb-level. This consists 
of an isosceles triangle of wood, from near the vertex of 
which a small plumb (see 38) is suspended. Through the 
point of suspension a sharp line is drawn at right angles to 
the base ; hence, if the free plumb-line coincides with this 
line on the triangle, the base of the latter will be horizon- 
tal. Base, 30 cm. ; height, 20 cm. ; thickness, 3 to 4 mm. 
suffices. 

By holding this plumb-level so that its base is in line 
with the free surface of the water in a beaker-glass, the 
plumb-line will be found to cover the line drawn on the 
wooden triangle. The same is true for the surface of 
mercury, alcohol, and, in fact, for all limpid liquids. 
Viscid liquids assume a nearly level surface only after they 
have, for a longtime, been at rest. 

117. ^sear the walls of the vessel, the surface of the 
liquid 18 not plane, but curved, either convex or concave. 
Observe the form of the surface of water in contact with the 
clean walls of the glass beaker, or a glass rod, a glass 
plate, in glass tubes of different diameters. Then dip a 
glass rod and glass tubes, the surfaces of which are thinly 

*You must not taste any of the bodies you work with, because many are 
poisonous. Also keep inflammable bodies (ether, gasolene,) far from any flame. 



Liquids. 63 



covered with a film of oil, into another glass with water, 
and observe the surface. Also dip another set of rods and 
tubes into a small vessel containing mercury. Xotice 
form, and measure the height or depression of the liquids 
in the tubes. Enter the result in your journal. 

If the diameter, d, of the tube, and the height, h, are 
accurately measured (both in millimeters) it is found that 
the product, hd, of height into diameter, is a constant for 
each liquid, but varying from one liquid to the other. 
In glass tubes, this product is in rilillimeters, for water, 
30.6 ; alcohol, 11.7 ; sweet oil, 15.0, and for mercury, 
—8.0. 

Accordingly, water rises 30.6 millimeters above the 
general level in a tube the diameter of which is 1 mm. ; 
and 61 mm. in a tube of 0.5 mm. bore. Since the change 
in level thus is very great, in narrow, that is, capillary 
tubes, it is usually [.termed ccqnlarity. Whenever the 
height of a column of liquid, in a tube, is to be meas- 
ured, the amount of capillarity must be taken into 
account. 

118. The free surfaces of any liquid contained in 
communicating vessels, coincide in the same level plane. 

A glass^tube about 10 mm. in diameter and bent in the 
shape of the letter IT, its two branches being about 20 
cm. long, is partly filled with pure water.* Whatever 
inclination you give to the tube, you will, by means of 
the plumb level (see 116), find both surfaces in the same 
level. Same experiment with another tube containing 
mercury. 

If, however, one of the branches is very narrow — 
only about 2 mm. in diameter, or less, — then the water- 
level will be 15 or more millimeters higher in the narrow 
tube than in the wide one. Why ? (See 117.) Make a 
like experiment with another tube containing mercury. 



*A few drops of a cochineal tincture may previously be added to the water in 
order that its surfaceman be more easily distinguished in the glass. 



64 Chapter III 



119- The shape of tube is altogether without influence, 
— except if the tube is so narrow that capillarity becomes 
of influence. This you can easily demonstrate by con- 
necting two glass tubes, A and B, by means of a rubber 
tube, R, filling the same partially with water, and ob- 
serving the surface of the water by means of the plumb- 
level (116) for all sorts of positions of the tubes A, R, B. 
Now take off one of the tubes, A, and replace it by a 
glass funnel, or a glass vessel of any shape, and repeat 
the observation with the plumb-level. 

120. Another U-shaped glass tube, constituting a pair 
of communicating vessels, contains sufficient mercury to 
fill the horizontal part, and also 5 or more centimeters of 
the vertical branches. Into one of the branches, a por- 
tion of another liquid, such as water, alcohol, sweet oil, 
has been poured. The laboratory should possess several 
such tubes (fig. 21), each containing a different pair of 
liquids. With each set follows a pipette (see 12) for the 
lighter liquid, and a small-stoppered vial with the same 
liquid. Each tube is attached to a vertical board fixed to 
a horizontal foot. To the vertical board a centimeter 
scale is attached between the two upright branches of the 
tube. A plumb-level serves to measure the height of the 
level in each of the tubes. 

It will readily be seen (by 118 and 119) that the mer- 
cury in the lower part of the tube, from the level A, be- 
tween the two liquids, to the same level, B, on the other 
side, balances itself. Hence the height, H, of the mercu- 
ry, above this level, balances the height, h, of the other 
liquid, above the same level. If the level A, between the 
two liquids, stands at a cm. on the scale, the free surface 
of the mercury at l> cm., and that of the other liquid at c, 
then you have evidently Il=b — a and h=c — a. 

Now, either add some more of the lighter liquid from 
the vial by means of the pipette, or take some away from 
the tube into the vial. Each time carefully measure the 



Liquids. 65 

levels, a, b, c, and therefrom find the heights, H and h, of 
the columns — accurate to the first decimal of the centime- 
ter. Make at least 10 such determinations; tabulate the 
results thus : — 

¥o. 1 a | b | c || H | h || h /n 

You will find that the quotient given in the last column 
is very nearly the same in all experiments with the same 
two liquids, take the mean of all single values. Hence 
these heights depend only on the nature of the liquids 
used. 

Now, either actually determine (see 29) the specific 
gravity, Gr, of the mercury, and the specific gravity, g, of 
the other liquid, or use the values marked on the appara- 
tus. Calculate the quotient G / g . You will find this value 
to be the same as the mean of the above quotients ; 
that is, — 

h G 

H~ g 

This proves : In communicating vessels, the heights, h 
and H, of liquids of different densities, g and G, are in- 
versely proportional to these densities. 

121. Since in any proportion the product of the means 
equals that of the extremes, we have, also, — 

g.h=G.H 
that is, in communicating vessels, the product of the speci- 
fic gravity of the liquid into- the height of the column 
(above the common level) is the same for both liquids. 

But these products express the weight of a column of 
liquid in grammes, if the section of the tube be one square 
centimeter, the heights being expressed in centimeters. 

The above, therefore, simply expresses, that the pressure 
on each square centimeter of the horizontal section at the 
common level, is the same downwards by the high column 
of lighter liquid, and upwards by the low column of heav- 
ier liquid, the latter pressure being transmitted with un- 
diminished force through the liquid filling the horizontal 
part of the tube. 
9 



66 Chapter III. 



Hence, in general, the pressure, p, at li centimeters 
below the free surface of a liquid of specific gravity, g, is, 
for each square centimeter of the horizontal plane, — 

p=g.h grammes. 

If water is used (g=l), it is h grammes ; if mercury is 
used (g=13.6), the pressure is (13.6) h grammes. If the 
same liquid is used, you need only give h and the name 
of the liquid to accurately determine the pressure, p. 

This method of determining a pressure by the height, h, 
of the column of some liquid, is of very general use in 
physical science. 

This pressure, p, is exerted equally in all directions, not 
only downwards, at the depth h. For if not so, the ex- 
treme mobility of the particles of the liquid (see 112) 
would permit the slightest inequality in pressure to pro- 
duce motions in the liquid, while here the liquid is at rest. 
The equal transmission of the pressure in all directions, is 
applied in the Hydraulic Press. 

122- Take a small prism of some metal (lead is very 
suitable) ; determine its volume, v, by direct measure- 
ment (see 28), and also by means of the graduated cylin- 
der (see 30). 

If now the metal prism is suspended by means of a hair 
or a thin thread, from a wire support, and completely im- 
mersed into a small beaker-glass containing water, the 
level of the latter rises, evidently, just as much as if v 
cubic centimeters of water had been added to the contents 
of the beaker. This fact has been made use of in the 
measurement of volume by immersion (30). 

Accordingly, the weight of the beaker, with water, must 
increase the same amount as if v cubic centimeters of 
water had been added ; that is, it must increase exactly v 
grammes. In this experiment, the metal prism must, 
however, be so suspended that it does not touch either 
the sides or the bottom of the glass. 

This reasoning is proved to be correct by accurately 
vjeighing the beaker, with water, both before the body is 



Liquids, 67 



immersed therein, and also while the body is ro immersed. 
The weight will be found to have increased by v grammes, 
exactly. See fig. 22. 

Perform this experiment, not only with the metal prism, 
the volume of which you can directly calculate from its 
linear dimensions, but also with several irregular bodies, 
such as iron nails, copper strips, etc. The general fact 
established by these experiments may be expressed in the 
following words : 

A vessel, containing any liquid, into which a suspended 
solid is immersed, without touching the vessel, increases in 
weight as much as the weight of the volume of liquid dis- 
placed by the immersed solid. 

123. But if the vessel with liquid increases this much 
in weight, the pull on the thread supporting the solid 
must be lessened by the same amount ; for nothing of the 
real weight of the body can be destroyed or absolutely 
lost. This consequence is readily verified by suspending 
the solid to one end of the beam of a balance, and 
equipoising the same ; when the solid, then, is immersed, 
the above given amount of weights have to be taken off 
the other scale-pan. We may express this fact as fol" 
lows : — 

A submerged body apparently loses so much of its weight 
as the weight of the volume of liquid displaced by the 
body. This fact is generally spoken of as Archimedes 
Principle. 

To directly verify this law, convert the balance into a 
so-called hydrostatic balance (fig. 23) by replacing the left- 
hand scale-pan by a piece of lead of exactly the same 
weight as the scale-pan. Suspend the body by a fine 
thread from the hook attached to the above counterpiece 
of lead. Then find w, the weight of the body (in air) > 
and also w', the weight of the same body when submerged 
in some liquid. Accordingly, l=w — w is the above loss 
or, in fact, the weight of liquid equal in volume to the 



68 



Chapter III 



volume, v, of the body. Determine this volume, v y by the 
graduated cylinder. Also determine (29) the specific gravity, 
g, of the liquid, wherein the solid was weighed. Then 
(see 25) g.v is the weight of liquid equal in volume to the 
volume of the body. Hence you must have — 
1 or w — w'=g.v 

This loss, 1, in weight, is also termed the buoyancy of 
the body for the liquid used. 

You may make a series of experiments Math several 
6olids and liquids. Tabulate your results in columns, 
thus : — 



Name of. 
Solid. | Liquid. 



w 


w' 


1 

w — w' 


g 


V 


g.v 



The d in the last column gives the difference, 1 — g.v, 
which will be found less than the unavoidable errors of 
the apparatus used. 

From this it also appears that the specific gravity of any 
solid will be obtained from w and w', and g ; for, accord- 
ing to the above, the volume of the solid is — 

w — w' 
v = 

g 
and, hence, its specific gravity, G, will be (see 25) — 

w 



w 

v w — w' 

If the solid is weighed in water, then g= 

w 



■1, and therefore 



w — w 
124- Take a prism of wood, about 5 cm. long, and 
having for its cross-section an equilateral triangle of about 
3 cm. each side. Weigh the same =w grammes. Then 
put it into a dish or beaker, with water; it wi\\ float, with 
one of its long edges downwards. Carefully notice how 
far it is immersed in the water ; let the breadth of the 



Liquids, G9 



wetted triangle be b cm. its height h cm. ; then the vol- 
ume, v', immersed is -J- h, ■£ b h, or x / 6 b h 1 cubic centime- 
ters, if 1 represents the length of the prism in centimeters. 
You will rind this volume, v', as many cubic centime- 
ters as the weight, w, of the entire prism is in grammes; 
that is — 

v'=7 6 b h l=w. 

Hence, the weight of this floating body is equal to the 
loeight of the ivater which it displaces. 

By repeating this experiment with other floating bodies, 
carefully determining the volume v' (in cubic centimeters) 
of the liquid displaced by the body, and also the weight, 
w, in grammes, of the entire body (in air), you will al- 
ways find these two numbers equal, so that the above 
result is a general law for all floating bodies. Express 
the same. 

If the body be of an irregular form, the volume, v', 
must be determined by a graduated cylinder (see 30). 

125. Take two small test-tubes, and three small cork- 
stoppered bottles, each provided with a small dropping 
tube, and containing, respectively, water, alcohol, and 
sweet oil. The specific gravity of these three liquids, is : 
water, 1.0; sweet oil, 0.9; alcohol, 0.8. 

Into one test-tube pour about one cubic centimeter of 
alcohol, and into the other about one cubic centimeter 
of water. To each add a drop of sweet oil by means 
of the dropping tube. You will see it sink in the alco- 
hol, but float on the water. Why ? 

Now pour the contents of the test-tubes together into 
one of them, and shake ; you will see the alcohol and 
water mix, but the oil form small globules, which but 
very slowly either rise or sink in the mixture. Accord- 
ingly, there is but a very small difference between the 
specific gravity of the oil and this mixture. 

If there is no difference at all, then the globules of oil 
will remain at rest in any part of the mixture. 



70 Chapter III. 



By this experiment it also is proved, that if a liquid is 
entirely free, or acted upon equally in all directions, it 
assumes the form of a sphere or globe. Such liquid globes, 
when small, are usually termed drops. We notice this 
form in the A?w-drop, the ram-drops — and in the shape 
of the sun, moon and planets, which really are but small 
drops in regard to the entire universe. 

III. MOLECULAR PROPERTIES OF GASES. 

126. A test-tube, not containing any solid or liquid, 
appears to be empty. But if you invert the tube, and 
bring its opening a few centimeters under the surface of 
water, you notice that the water does not stand as high in 
the tube as outside the same. Hence, there is some sub- 
stance in the tube which resists the water (compare 118). 
This substance is air, usually further specified as atmos- 
pheric air. It thus, also, possesses magnitude (1), like all 
other bodies. 

If you now turn the tube with its closed extremity 
down, until this extremity is a little below r the level of the 
opening, — which remains a few centimeters below the free 
surface of the water, — you will notice the air escape from 
the tube, through the water, in round globes (Rubbles). 
The tube will entirely fill with water as the air escapes. 
Hence, air is much lighter than water. Compare 120 
and 33. 

127. Now again turn the tube up, always keeping the 
mouth of the tube under the surface of the water. You 
will now find that the water remains in the tube, entirely 
filling the same. Figure 24. 

Hence, there is some pressure exerted on the free sur- 
face of the water in the larger vessel ; for otherwise the 
level would be the same in these two communicating 
vessels, A and B. See 118. 

This pressure on the free surface of the water in A, can 
only be produced by some body resting thereupon. But 
air does rest upon this surface (126). Hence, this air 
exerts some pressure. Consequently, air possesses weight. 



Gases. 71 



Blow air into the tube by means of a narrow glass tube; 
the air will collect in the upper part of the inverted tube, 
and the volume of the air introduced may be measured in 
the usual way (11). This is the common way of collecting 
and measuring gases. 

128. The magnitude of this pressure of the atmosphere 
can be ascertained by taking longer and longer tubes for this 
experiment. Pascal found, in 1646, that a tube of about 
12 meters did no longer remain filled with water ; upon 
inverting the tube he observed that the column of water 
always sunk until it stood in the tube B, 1033 cm. (i. e. 10-J- 
meters), above the free surface of water in the open vessel, 
A. 

Accordingly, the pressure of the atmosphere is equal to 
the pressure of a column of icater 1033 centimeters high. 
See 121. Hence, this pressure is 1033 grammes on each 
square centimeter. 

It had, long before, been noticed that water could not 
be raised more than about ten meters by suction pumps. 
Why not ? 

129. Above the level of the water, in such a tube, 
there is apparently nothing, for there is neither water nor 
air, the only two bodies operated upon. 

Such a space, which is apparently empty, is called a 
vacuum. 

130. The experiment of Pascal^ described above (128), 
cannot well be repeated by the student, because, so long 
a tube is unwieldy. But the experiment can be repeated 
by means of a tube less than one meter long, if mercury 
is used instead of water ; for a column of mercury, exert- 
ing the same pressure as a column of water 1033 cm. high, 
will only have a height, h = 1033 /g 3 if g=13.6= the spe- 
cific gravity of mercury (see 121). You will find h=76 
cm. Hence, also : The pressure of the atmosphere is equal 
to the pressure of a column of mercury 76 cm. high. 



72 , Chapter III. 



Thia was first aecerl ined by 'Torricelli (pronounced 
r i or-ree-tchel'-lee), in 16i ( J. Hence, the vacuum above the 
mercury, in this tube, is often called Torricelli 's vacuum* 
and the experiment itself Torricellih experiment. The 
experiment should not be repeated by the beginner except 
a strong tube be used, and the work-table provided 
with properly raised edges, to prevent any spilled mercu- 
ry from tailing on the floor. If, however, a little mercury 
should be spilled on the floor, notwithstanning these 
precautions, it should be carefully taken up* by a 
iriercury sponge; that is, by a piece of sheet zinc, 
which has been dipped into diluted sulphuric acid. 
Such zinc will readily take up mercury drops. The mer- 
cury thus taken up has become zinc-amalgam, and must 
not be added to the pure mercury, but be k<'pt in a sepa- 
rate vessel. 

The experiment described is simplest made by first 
entirely tilling the tube (about 85 cm. long) with mercury, 
then closing the opening firmly with the thumb of the 
right hand, and thereafter inverting the tube with the 
thumb, under the surface of the mercury contained in a 
small glass vessel. Upon now removing the thumb, the 
mercury will sink until it stands about 76 cm. above the 
level of the mercury in the glass vessel. 

131. In order that the pressure of the atmosphere can 
be accurately measured by the height of the column of 
mercury, Torricelli? s experiment must be performed with 
great care. The tube should be at least 8 mm. wide 
(why? see 117). and the mercury, as well as the tube, 
should be entirely free from air.f The last condition is 
usually fulfilled by boiling the mercury in the tube, — an 
operation of great difficulty. When the experiment has 
been thus ( arefully performed, the filled tube and mercury 
vase constitute a Barometer / usually a millimeter scale is 
attached to the support of this apparatus, in order to 
directly read oft' the height of the column of mercury. 

•Mercury left on the floor will poison the room. 

fWhether this is a fact may be ascertained by .slowly inclining the closed end 
of tho tube; if, in this manner, the tube is entirely filled with mercury, without the 
least bubble of air remaining at the top, the tube is really free from air. 






Gases. 73 



132. This height, h, of the barometer, changes at any 
one place with the condition of the weather.* The barom- 
eter sinks when rain and storm approach, while it rises 
with the advent of fair weather. The average height 
near the level of the sea is, however, 76 cm. or 760 mm. 

If we ascend a mountain with the barometer, we iind 
the column of mercury sinking ; for all the air below the 
mercury surface, in the open vessel, cannot press upon 
this mercury. Hence, the height, H, of the mountain, 
can be ascertained by observing the height, h, of the 
barometer at the foot of the mountain, and also the height, 
h', on the top of the mountain. It has been found that 
(approximately) — 

h — h' 

H=16,000 meters. 

h + h 

133, A bent tube is called a siphon, when it is used 
to transfer a liquid from one vessel into another. The 
most convenient siphon for the student's use consists of a 
rubber tube, about 30 cm. long and 5 mm. wide ; by in- 
serting straight glass tubes (each 10 cm. long) in its extrem- 
ities, this siphon is easier handled. 

First, fill the siphon with the liquid to be transferred ;f 
then, while closing the two openings with the fingers, 
insert the same into the two vessels. The siphon is now 
ready for its work. 

To understand the action of the siphon, let the siphon, 
D, be inserted into two beakers, or tumblers, containing 
water up to the same level, A and B. Figure 25. Then 
the insertion of the siphon cannot change this level (see 
118). jlSTow lower the vessel, B, so that the surface of 
the water therein stands at C. Then the water will, 
from A, flow to C, to restore the level, for A and C are 
vessels communicating by the siphon, I) (118). 

*Have each student observe the barometer at a stated hour during one week, at 
least, and record the observations in his journal. 

•{-This is easily done by immersing the whole tube in the liquid,— or by directly 
pouring the liquid into the siphon while holding the openings of the siphon 
upward. 

10 



74 Chapter III. 



134. In the position, ADB, we can most readily ascer- 
tain the limit to the height, AD, of the siphon ; for 127 and 
12S show that this height must be less than a column of 
the liquid balancing the pressure of the atmosphere on the 
free surface in A or in D. Hence, for water, this height, 
AD, of the siphon, must not exceed 1033 cm., and for 
mercury not 76 cm. (see 130). 

In the position, AD'C, this limit applies only to the 
branch, AD' ; for, if the pressure of the atmosphere only 
keeps this branch, AD', overflowing into D'C, and the 
latter was filled at first, the liquid will continue to flow 
out at C, even into the air. 

135. The velocity of the flow through a siphon, AD'C, 
figure 25, is dependent on the difference in level, AC, if 
the lower extremity of the siphon is immersed, as in the 
figure. Otherwise the velocity depends on the difference 
in level between the surface, A, and the orifice of the 
lower branch of the siphon. 

Connect two wide flasks by a siphon ; mark a volume 
of about 500 cc. on one of them. By proper change in 
level, make the liquid stand exactly at the lower mark in 
this flask. Then, by the pressure of some clamp* on the 
rubber tube, stop the flow. Place the level in marked 
flask a measured distance, d, below that in the other. 
Open the clamp, and count the number, n, of seconds 
(see 39) which it takes the water to ieach the upper 
mark ; then clamp again, and also measure the difference 

in level. The mean of these two values may be taken 

d_i_d' 
as the average difference in level, T>= ( • You. will 

find that n \/D is nearly constant. What does this prove 
in regard to the relation between the velocity and the 
difference in level ? 

136. The siphon may be utilized to form a simple 
Aspirator, fig. 26, which also can be used as either an 
exhausting or a condensing air-pump. 

♦The common nprin^ clothes-pins will answer well. 



Gases. 75 

The two flasks, A and B, of equal capacity, should hold 
at least one liter each. They are connected by a siphon, 
mainly consisting of a rubber tube, 2 to 5 mm. diameter. 
The glass tube extremities of this siphon pass, air-tight, 
through corks, together with the short tubes, a and b. 
The joints at the corks should be made quite air-tight, if 
necessary, by means of some sealing-wax. One of the 
flasks, A, is filled with water before sealing the same. By 
suction at b, the siphon is filled also, and the aspirator is 
ready for use. 

Put the full flask, A, on some square blocks, and the 
water will flow, through the siphon, into B. After B has 
filled, reverse the position of the flasks, and the water will 
flow back to A. 

If a greater difference in level is required, the rubber 
tube must be longer, and the upper flask must be placed 
on some shelf, etc., while the lower may stand on the 
floor. 

137. If A is full, and stands above B, as in fig. 26 
the water flows down from A to B. If, now, a is connect- 
ed with some other apparatus, F, such as a flask, etc., air 
will be drawn from F to fill the space vacated by the 
water in A. Thus the apparatus acts as an Aspirator; 
or, if the difference in level is great enough, as an exhaust- 
ing air-pump. 

If the rubber tube connecting F with a is provided with 
a spring clamp, close this when A is nearly empty, trans- 
fer B to the place of A, and connect F with b; upon 
opening the spring clamp, the process of exhaustion will 
continue. 

A flask, F, connected with b, in the lower flask, B, 
will receive the air expelled from B by the water flowing 
down from A. Hence, this apparatus acts in this way as 
a condensing air-pump. 



76 Chapter III. 



138. A smaller apparatus of this kind, but containing 
mercury instead of water, will be 13.6 times as effective 
for the same difference in level (see 121). But, in regard 
to such an apparatus, the remarks made in 130 apply. 
However, some of the very best air-pumps of recent 
invention are mercury air-pumps ; such are the Geissler 
air-pump, and SprengeVs pump. The famous Bunsen 
air-pump, used so much in chemical laboratories, works 
by w^ater running down a tube of 5 to 10 meters. 

139. The older air-pumps are constructed essentially 
like common water-pumps, from which they differ mainly 
by the much greater accuracy of the workmanship. In 
all of these pumps, mechanical force is applied by means 
of levers or other machines, while in the preceding 
pumps (137), the motor is some flowing liquid. The 
mechanical air pump was invented by Otto von Guerrcke, 
about 1650, in Madgeburg. 

A few of the common, simple, qualitative experiments 
with such an air-pump, should be exhibited before the 
students by the teacher, if the apparatus is accessible. 
The most important of this apparatus is : — 

1st. The Madgeburg Hemispheres, showing that the 
pressure of the atmosphere is considerable in all di- 
rections. 

2d. The Hand Glass, used to exhibit the pressure of 
the air on the human body. 

3d. The hollow copper — or glass globe, — used to 
prove that air possesses weight. 

140. The compressibility of air may be observed and 
approximately measured, by slowly pressing an inverted 
bottle, with narrow neck, from the surface of water in a 
beaker to the bottom thereof. It will then be found that 
the level of the water rises considerably from the mouth 
of the bcttle toward the interior of the bottle. 



Gases. 77 



Upon lifting the bottle up again, the water will recede 
from the neck, so that the air in the bottle now expands, 
exactly as much as it was compressed before. Hence, 
atmospheric air is perfectly elastic. 

141. Sound is transmitted through the air because of 
the elasticity of the air. One of the simplest ways of 
producing a regular sound, or a tone, is by gently blowing 
obliquely into a closed tube. A glass tube, closed below 
by means of a cork, will answer. 

If the cork fits the tube, so that by means of a small 
wooden rod the cork can be moved up or down the tube 
with gentle friction, you have what is called a closed pipe. 
The length, 1, of such a closed pipe is the distance from its 
month (where you intonate the same) to the bottom. You 
will observe that the tone becomes more acute as you 
shorten the length of the pipe, and more grave as you 
lengthen the pipe. 

142. To ascertain the numerical relation between the 
length of a closed pipe and the tone which it gives, you 
need only two small glass tubes, each about 20 cm. long 
and 7 to 10 mm. in diameter, both provided with a mov- 
able cork bottom. 

In one of the pipes, keep the cork bottom at the same 
place ; call the tone it gives, the First. In the other pipe, 
move the bottom until the toi>e is exactly the first (I.), 
second (II. ), third (III.)? etc., in regard to the fundamental 
First given by the other pipe.* For each tone, carefully 
measure the length of the pipe. Record these measure- 
ments, T, for the rising scale, I., II., III., IV., etc., and 
repeat the same measurements for the descending scale, 
1", VIII., VII., VI., V., etc. 

Of these independent values, 1' and 1", take the mean 
and add the diameter of the glass tube ; call this sum 1. 

*If the student is not sufficiently musical, let him associate in the work with 
some other student who is musical. 



78 Chapter III 



Also, divide each of these values, 1, into that of the first, 
or fundamental; the ratio, r, thus obtained, is recorded 
with two decimals only. The true values of these ratios 
are, according to theory, — 

7i, 9 / 8 , 5 A, 4 / 3 , V* 5 / 3 , l % »A, 

which values you convert into decimals in the next 
column, headed r'. Subtract the values, r, observed by 
you from these theoretical values, r', and record the differ- 
ence in the last column as your error, e = r' — r. The 
record will therefore appear under the following heading : 



Tone. 



LENGTH. 



1' 1" 1 



RATIO. 



ERROR. 



Instead of the names, first (I.), second (II.), etc., above 
employed, musicians use the following nomenclature for 
the tones : — 

Ordinals : L II. III. IY. V. VI. VII. VIII. 

German: CDEFGA H C. 

Anglo-German; CDEFGA B C. 

Anglo-Italian : Do Re Mi Fa Sol La Si Do. 

Italian : Ut " " " " " " Ut. 

143. To make the regular air-waves of a tone appar- 
ent, take a glass tube about 50 cm. long and one centime- 
ter in diameter, closed at one extremity by a cork stopper, 
and at the other extremity connected with the head of a 
common tin whistle, by means of a rubber tube, or in any 
other way. The perfectly dry interior of the tube has 
been very thinly coated with perfectly dry, finely pulver- 
ized silica.* Intonate the whistle so that the tone remains 
of the same pitch, and, while it resounds, gently tap the 
horizontal tube with a knife. If the experiment was per- 
formed with sufficient care, you will see the silica move 

♦Obtained by igniting and pulverizing precipitated silicon dioxide. 



Solids. 79 



in the tube while the tone resounds, and upon the cessa- 
tion of the tone the silica will be found arranged as 
indicated* in figure 27. It forms regular, transversely 
striped accumulations in equal distances from one another. 
Measure these distances yourself; they are equal to one- 
half a wave length of the tone produced. 

These figures are very beautiful, and evidently are the 
markings of the air-wave which moved in the tube while 
the tone was heard. These figures form, indeed, ^picture 
of the tone, drawn by the tone itself. 

IV. MOLECULAR PROPERTIES OF SOLIDS. 

144. Solids are bodies whose particles are not readily 
movable amongst one another (112). Hence, solids retain 
their form with considerable power. Under certain cir- 
cumstances, solids even spontaneously assume a form spe- 
cifically peculiar to themselves (see Section V. and VI. of 
this chapter) ; such solids are called crystals. 

145. When acted upon by a sufficient force, the parti- 
cles of solids do move (114) more or less. If the form, in 

'this manner, can be changed considerably, the body is 
flexible ; and if, upon the cessation of the force, the body 
resumes its original form, it is elastic. If the body readily 
yields under the hammer, it is malleable / if it can be 
drawn through smaller and smaller holes, so as to change 
its form into that known as wire, the body is ductile. In 
order that a body can be ductile, it must evidently have 
both malleability and tenacity. Tenacity is the resistance 
of a solid against rupture by traction. 

If the solid does not change the position of its particles, 
but rather breaks to pieces, it is not malleable, but brittle. 
The shape of the new surfaces formed is called the fracture 
of the body. If these fractures are quite plane and smooth, 
they are called cleavage planes, and the body is said to have 
cleavage, — a property peculiar to crystalized matter. 



80 Chapter III. 



The resistance which a solid offers to another entering 
into it, is called its hardness. A solid easily penetrated is 
said to be soft. 

We shall now study these properties of solids more in 
detail, by appropriate experiments. Only crystal-form 
and cleavage will be studied separately in a subsequent 
section (VI). 

146. Flexibility and Elasticity. Frame a definition 
(145). Test the following solids, preserved in a small 
box, for these properties, and enter the result of your ob- 
servation in your journal. Also, estimate the degree to 
which these properties are possessed by the bodies at 
hand : — 

Rubber. Wood (small prism). Ivory. Whalebone. 
Steel. Brass. Copper. Iron (soft). Zinc. Lead. Glass ; 
a rod and seme very thin fibres. Chalk. Clay. 

147. Malleability / Brittleness / Fracture/ Cleavage. 
To ascertain malleability, take a small grain (about one 
cubic millimeter) of the body, and let a small hammer 
descend upon the solid, which rests upon a small anvil. 
Avoid the hammer's flying back. Examine the result by 
means of a magnifying glass. If need be, take, also, a 
larger piece of the substance. For the kind of fracture, ■ 
observe the larger piece given. Planner's hammer and 
anvil are the best adapted to this work. This anvil is a 
rectangular plate of about 5 by 3 by 1 cm. ; the hammer 
is in proportion. But a common pocket-knife will answer ; 
a brittle substance will break, while a malleable solid 
will flatten when pressed by the knife-blade against a 
piece of paper resting on the table. 

For practice, cut off a small piece from wire of lead, 
iron, silver, brass; from plate of zinc, tin; from various 
oilier solids, such as blue-vitriol, rock-candy, calcite, etc. 
All these bodies are to be kept in a box, together with 
hammer and anvil. Note the results, as usual. 

148. Solids which are not malleable can be divided 
by grinding them in mortars. This operation is called 

pulverization, and is of the utmost importance for many 
purposes. 



Solids. 81 



Larger pieces of such solids are wrapped up in clean, 
strong writing paper, and broken into smaller fragments 
on an anvil by means of a few strokes of a hammer ; the 
fragments thus obtained are pulverized in a mortar. 

Mortars are made of steel, bronze, iron, porcelain, glass, 
and agate. They are of various shapes and very different 
sizes. The pestle is somewhat hemispherical below x and 
this part of the pestle is made to describe circles in the 
mortar; thereby the intervening parts of the solid are 
ground or triturated until they are sufficiently fine. Only 
in the larger metallic mortars are blows combined with 
the grinding. 

149. The pulverized substance often appears to have 
a color different from the unbroken solid ; and, as a rule, 
the color of the powder is much lighter than that of the 
solid. 

The color of the powder is called the streak of the body. 
For many bodies the streak may be observed by pulver- 
izing not more than a cubic millimeter of the substance on 
white paper by means of the pen-knife. 

Determine the streak and color of potassium bichro- 
mate, blue vitriol, green vitriol, alum, and some other 
bodies. 

150. Hardness. From the definition given in 145, it 
appears that one body is harder than another, if the latter 
is scratched by the former. Thus, copper you w T ill find 
harder than the finger-nail; glass harder than copper, and 
a good steel file harder than glass. For the sake of con- 
venience, 10 degrees of hardness have been adopted, of 
which the above solids determine the following: — 

Degrees of hardness : 1 3 5 7 

Name of solid : Finger-nail. Copper. Glass. File. 
The letter H is used as an abbreviation of hardness; 

thus, H=7 means : Hardness equal to 7, or to that of the 

file. 

11 



82 Chapter III. 



To determine the hardness of any substance, we press 
our nail on it while taking the substance into our hand. 
If the nail fails to make any impression whatever, the 
hardness of the substance is above 2. Next take the file; 
suppose it makes a deep furrow when drawn across some 
blunt edge, the hardness is much below 7. If, next, the 
substance fails to scratch glass, its hardness is even below 
5. If it scratches copper, its hardness is above 3. Conse- 
quently, the hardness of this body would be about 4. 

In this manner the hardness is always readily deter- 
mined, if you also observe, that two substances, which 
mutually scratch one another, are equal in hardness. 

For practice, determine the hardness of the following 
minerals : — 

Apatite; Calcite (calc 6par) / Feldspar ; Fluorite 
(fluorspar) / Gypsum / Quartz (rock crystal) / Talc / 
Topaz. Enter the result in your note-book, and learn it 
by heart for further use. 

These eight minerals constitute the first eight degrees 
of hardness (1 to 8) in 3lohs i Scale of Hardness, adopted 
by all mineralogists. They are surpassed in hardness by 
the Ruhij (11=9) and the Diamond (11=10). The last 
two bodies are 4 harder than any other known body, so that 
the diamond is the hardest of all bodies. 

True gems have a hardness above 7. They are sold by 
the carat, which averages 0.2 grammes. The Amsterdam 
carat is 0.208 grammes, while the Florence carat is 0.197 
grammes. 

V. SOLUTION AND CRYSTALLIZATION. 

151. Iu 113 it was shown that the state of aggregation 
of bodies can he changed by means of heat. By the addi- 
tion of heat, many solids being converted into liquids 
{fusion) and then again into gases {volatilization), while 
by the loss of heat in cooling, gases may become liquids 



Crystallization. 83 



(liquefy) and liquids assume the solid condition of matter 
(solidify). These processes will be studied more in detail 
in the second volume. 

But the state of aggregation may also be changed by 
mixture. The solid sugar gives, when mixed with liquid 
water, a liquid mass ; so, also, salt and many other bodies 
give rise to liquids with water. 

152. Solution is the conversion of a solid into a liquid 
by means of a liquid. The dissolving liquid is called the 
solvent / the resulting liquid is called the solution. 

The solvent most commonly used is water ; but alcohol, 
ether, bisulphide of carbon, and many other liquids, are 
also used at times. 

A solution is said to be saturated when it does not dis- 
solve any more of the finely pulverized solid introduced 
into it. If it can take up much more of the solid, the solu- 
tion is said to be dilute; if it can dissolve but very little 
more, the solution is said to be concentrated. 

153. The solubility of a substance is the weight in 
grammes of the solid which one gramme (1 cc.) of the sol- 
vent requires to form a saturated solution.* 

Thus one cubic centimeter of water forms a concentrated 
solution with OA gr. of salt ; hence the solubility of salt 
in water is 0.4. So, also, the solubility of sugar in water 
is 2.0, because 2 grammes of sugar are required to convert 
one cubic centimeter of water into a saturated solution. 

154. To free a solution from an excess of the solid, it 
may be filtered through porous, unsized paper (filter paper)- 
By this same operation of filtration any solid impurities 
may be removed from the solution. 

The filter paper is cut into circular filters. Each such 
filter is folded first into halves along one diagonal, and 
thereafter this double semi-circle is again folded at right 
angles to the first diameter, so that the filter is folded up 
to the size of a fourth of a circle. Put this folded filter 

•If the solubility of a solid is less than 0.002 (that is 2 mill! grammes in each cubic 
centimeter of the solvent), the substance is irractically insoluble. Such substances 
are, accordingly, called insolubU. 



84 



Chapter Iff. 



carefully iato the properly supported glass funnel, so that 
three thicknesses of the paper are on one side and one 
thickness on the other. * iNow moisten the filter with a 
little of the solution (or with the pure solvent) and slowly 
pour the solution to be filtered on the paper along a glass 
rod held slanting against the rim of the vessel from which 
the solution is poured out. 

155. The following table of solubilities of a few very 
common substances in water will prove useful to the stu- 
dent for reference : — 



JNAME OF SUBSTANCE. 



VULGAR. 



SCIENTIFIC. 



SOLUBILITY IN 
WATER. 

ALM08T 
BOILING. 



Sulphate of Potassa 

Nitrate of Baryta 

Common salt 

Yellow Prussiate of Potassa.. 

Chlorate of Potassa 

Sal Ammoniae 

Bichromate of Potassa 

Nitrate of Lead 

Blue Vitriol 

Nitre (Saltpeter) 

Chili Saltpeter 

Green Vitriol 

Alum 

White Vitriol 

Rock Candy 



16 smlphate. of Ammonia and Iron 



Potassium Sulphate 

Barium Nitrate 

Sodium Chloride 

Potassium Cyano-ferrate.. 

Potassium Chlorate 

Ammonium Chloride 

Potassium Bichromate 

Lead Nitrate 

Hydrated Cupric Sulphate 

Potassium Nitrate 

Sodium Nitrate 

Hydi ated Ferrous Sulphate 

Alum 

Hydrated Zinc Sulphate 

Sucrose 

Hydrated Arnmonio-ferious Sul- 
phate 



0.1 

0.08 

0.36 

0.25 

0.1 

0.35 

0.13 

0.5 

0.42 

0.3 

0.3 

1.0 

0.15 

i.<; 

2.0 
0.36 



0.26 

0.35 

0.40 

0.50 

0.6 

1.0 

1.0 

1.1 

2.0 
2.5 
2.5 
2.7 
?.6 
6.5 
5.0 

1.0 



light 



156. Determination of the solubility. Take a 
porcelain dish, or even a glass dish ; weigh the same = d 
grammes; put into the dish some cubic centimeters of the 
saturated solution, f and weigh again = a. Then carefully 
evaporate the solvent by heating the dish on the water 
bath.j: When the residue is quite dry, weigh again =b. 
From these three weighings you obtain the solubility 



M'ho upper margio of the filter should remain about one cm. below the rim of 
the tunnel. Never fill the liquid up to the margin ol the filter. 

ionizations spoken of in the next section, enough of residual 
in saturated Btate will remain. They should, for each substance sepa- 
ly, be kept In properly labeled bottles for this special purpose. Lead Nitrate, 
ai Bichroi good for this purpose. The residue ob- 

tained should also I ed in a w ide-mouth bottle, for further crystalliza- 

:oiii. 

ovided with a circular opening for the support of the 
. is quite sufficient Be careful that the surface of the water in this water-bath 
doe§ not <£et too low. 



Crystallization . 8 5 



S = ~b because the amount of residueis evidently = b— d, 
and amount of the solvent = a— b. 

157. The solubility of most substances is greater in the 
hot than in the cold solvent, as appears in the table (155). 
To prove this, take of the finely pulverized solid nearly as 
much as its solubility in boiling water, given in 155; add 
one cubic centimeter of water to this solid in the glass 
test-tube, and shake ; you will notice that much of the solid 
remains undissolved. 

If you now carefully heat the contents of the test-tube 
in the flame of a common alcohol glass lamp, or put the 
tube into boiling water, the solid will soon dissolve. 

158. If you now put this hot concentrated solution 
aside, it will soon cool down. But at the same time that 
amount of the solid will separate in the solid condition, 
which was dissolved in excess of the solubility of the sub- 
stance at common temperature. 

Thus if you had prepared a hot concentrated solution of 
2 grammes of alum in 1 cq. water, at least 1.5 grammes 
of this alum must separate again from the solution while 
the hot solution cools ; because at common temperature 1 
cc. water can only dissolve 0.15 grammes of alum (155). 

159. If the hot concentrated solution is cooled very 
slowly », the particles of the solid in solution separate slowly 
from the solution, and build up regular, very beautiful 
forms, called crystals. This process is called crystalliza- 
tion by cooling. The substances ]STo. 1, 2, 5, 7, S, 13, in 
155, very readily crystallize ill this manner ; beautiful 
crystals are obtained from 10 to 25 cc. of solution.** 

The student should prepare the solution himself. Measure the amount of water 
you take. The table in 155 will show how much of the solid is required to form a 
hot concentrated solution; less than the figure in the last column. The solid should 
be finely pulverized (148; in a porcelain mortar. Solution is effected^ while the dish 
or beaker glass is heated on a sand-bath, i.e. a shallow iron pan containing sand. 
The glass or porcelain vessel should be quite dry on the outside before it is put on 
the sand ; heat is applied gradually. To prevent evaporation of the water, cover the 
beaker or dish with a large watch-glass; otherwise you must gradually replace the 
evaporated water. 

It is evident that the solution will cool more slowly if left on the hot 5and-bath, 
from which only the flame i§ removed; hence in this manner you obtain the beet 
crystals. 



86 Chapter lit 



If a fine thread is stretched through the cooling liquid, 
fine crystals will grow on this thread. 

160. Common salt cannot be crystallized by cooling ; 
for the difference in solubility is too small — only 0.0.4 
(See 155.) But good, although small, crystals of salt are 
obtained by exposing a cool, concentrated solution to spon- 
taneous evaporation — that is, to evaporation at common 
temperature in an uncovered vessel.* 

TJie method of crystallization by spontaneous evapora- 
tion gives, usually, the finest crystals; but it is much 
slower. The substances No. 3 and 11 (155) are good exam- 
pies. 

161. This method is also made use of to obtain micro- 
scopic crystals. A small drop of the solution is put upon 
a clean glass side and distributed over the same, so as to 
form a very thin layer only.f If you now watch this spot 
through the microscope, you will see fine and numerous 
crystals form in the same. 

A good magnifying glass will answer pretty well if there 
is no microscope at hand. 

The crystallizations of No. 6 and 10 in 155 are especially 
beautiful under the microscope. 

While observing these crystals, the student should, as 
accurately as possible, draw a figure of at least a few of 
these microscopic crystals in the journal. 

162. Crystals having a diameter of 5 millimeters are 
abundantly large for all purposes of study here to be re- 
quired. Much larger crystals may be formed, by the method 
described ; but the smaller crystals are, on the whole, the 

*'>ftcn the solution creeps, especially during spontaneous evaporation; that is, a 
mist of the solid forms above the liquid, and grows higher and higher up, until it 
finally passes all over the vessel, even to its outside. This is easily prevented by 
giving the Teasel a thin coating of lard or oil at a email distance above the level of 
the solution. 

ISmall cork-stopped vials containing the saturated solution should be kept for 
this purpose in a box, together with a few glass slips. The student then only needs 
to moisten the cork by inverting the vial, and to touch the slide with the moistened 
cork in order to transfer enough of the solution to the slide. 



Crystallization. 87 



best. Beginners soon learn to distinguish all parts on 
much smaller crystals, at least by means of a magnifying 
glass. 

163, Small crystals are best handled after they are 
mounted* The simplest way is to put a very small bit of 
bee's wax on the head of a pin, and then to press the lat- 
ter against that point of the crystal which is to be sup- 
ported. We, of course, select that point of the crystal 
which is least well developed. 

If the crystal is very small, it is best to cut off the head 
of the pin, and to mount the crystal on the blunt end of 
the brass wire thus remaining. 

164. The mounted crystal is preserved by putting the 
pin into the cork stopper of a small glass specimen-tube.^ 
The best dimensions of these tubes are 45 mm. long and 
15 mm. wide, or 10 mm. wide. More than these two sizes 
are but rarely required. 

Fig. 28 shows such a specimen in one-half natural size. 
It will be noticed that only the upper half of this crystal 
is well developed. 

A strip of thin paper, 1 cm. wide, is pasted around the 
open end of the specimen-tube, to serve as label. The 
name, etc. of the crystal is written on this label ; also by 
whom the crystal was prepared, or from whom obtained. 

A number of such mounted crystals may be preserved 
in a tray or case, forming a beautiful cabinet or collection 



*For the beginner, a few crystals should separately be mounted on a card, by 
means of bee's wax or sealing wax, and on the same card a figure of the crystal 
should have been drawn by the teacher. This figure should represent the crystal 
precisely as it appears when facing the card; i. e. it should give a horizontal projec- 
tion of the crystal (see 75). 

f Instead of these somewhat expensive tubes, these corks may, by means of seal- 
ing wax, be fastened to small wooden blocks, on the front side of which the paper 
label is pasted. Blocks 5 cm. long, 3 cm. wide, and 5 mm. thick, of cherry wood, 
will answer. 

Or, cheaper still, the corks may be fastened to one larger board, which thus may 
hold the entire collection. If each pin carries a number on a piece of paper through 
which It passes, the labels may be dispensed with, if the crystals are catalogued, after 
these numbers. 

t 



88 Chapter III. 



<>/ crystals. "By preserving the best crystals obtained by 
the practising students, the school soon acquires a good col- 
lection of this kind. 

165. In addition to the artificially crystallized sub- 
stances enumerated in 155, it is desirable to possess a cab- 
inet of native crystals, or crystallized minerals. The fol- 
lowing list contains the most instructive specimens which 
also are most easily procured from dealers in minerals. 
Those in italics should be preferred, if all cannot be pro- 
cured : — 

SCIENTIFIC NAM*. VULGAR IfAMB. 



8 



10 

11 

12 
13 

H 



Pyrite | Iron Pyrites, Fool's Gold. 

Galenite Lead Glance, Galena. 

Fluorite i Fluor Spar. 

Magnetite -.* | Magnetic Iron Ore. 

Garnet. 

Chalcopyrite » ' Copper Pyrites. 

Rutile. 

Cassiterite , Tin Stone. 

Barite « ; Heavy Spar. 

Celestite^ 

Aragonite. 

Topaz. 

Sulphur. 

Mica. 



15 Calcite Calc Spar (several specimens). 

16 ; Quartz Rock Crystal. 

11 Heryl. 

18 | Turmaline. 

19 Hematite Red fron Ore. 

20 j Gypsum. 

Orthoclase Feldspar (Potassium). 

Pyroxene, or Augite. 

Amphibole '. Hornblende. 

24 i Albite > Feldspar (Sodium). 

Axinite, 



VI. CRYSTALLOGRAPHY. 

166. Upon examining any of the crystals, either in the 
cabinet of artificial or native crystals, it will be seen that 
all crystals are hounded by plane surfaces. But it also will 
be remembered that the crystals assumed their peculiar 
form spontaneously (159). Hence we obtain the following 
definitions : — 

A CRTS' a polyhedron formed spontaneously by its 

own particles. 

Crystallography is that branch of physical science 
which treats of crystals, especially the form of crystals. 



Crystallography . 89 



167. The planes bounding the crystal are called fa ces. 
The line wherein two adjacent faces intersect is called an 
edge. The point formed by the intersection of three or 
more faces is called a corner. 

The angle formed by any two edges in the same face is 
called a facial angle. The angle formed by two faces at 
their edge is called the interfacial angle of the faces ; it is 
the inclination between the two faces, and equal to the 
angle between two lines drawn in the two faces from the 
same point of the edge at right angles to the latter. 

The several faces meeting in one point constitute & pyr- 
amid. Faces which intersect in parallel edges constitute 
a zone on the crystal. * 

168. For the sake of easy reference, some system of 
notation must be used. The following is, perhaps, the 
simplest for beginners, and will be used in the subse- 
quent : — 

A face is denoted by a letter; see figure 29, which rep- 
resents a crystal of blue vitriol. On the side fronting the 
observer the faces are denoted by roman letters ; on the 
opposite side italics are used. The student should him- 
self make a drawing of a crystal as seen from above and 
the right,f and enter the letters on this drawing. Com- 
pare 75. 

Which letters to select is arbitrary. Rauy selected the 
initials of the three syllables in the word Pri-Mi-Tive to 
denote those three faces which appeared to him to con- 
stitute the primitive form of the crystal. The faces M and 
T a*e placed vertical, and P is either horizontal or inclined, 
constituting the base of the prism MT. 

169. By a closer inspection it is found, that for each 
face on the front side there is another face on the opposite 



*Trace these parts of crystals on any one crystal ; a crystal of blue vitriol is 
especially adapted for this purpose, because its form is so simple. 

tlf need be, close one eye while obserring the crystal. 

12 



90 Chapter III 



side exactly parallel thereto. Thus on blue vitriol the faces 
P, M, T have their parallels. It is, of course, proper to 
denote these faces by the same letters (in italics) as those 
used for their parallel faces in front (roman). Thus, on 
the blue vitriol crystal we have P, M, T in front, and the 
three faces parallel to these, 1\ M, T. 

Only in case the crystal is broken, or by some obstacle 
was prevented from growing in all directions, the parallel 
face will be absent. Hence it is customary to apply the 
term face to even the pair of parallel faces, such as P 
and P. 

170. The interfacial angle is, in drawings of crystals, 
denoted by letters inscribed on the faces. ThusP n is the 
angle formed between the faces P and n (figure 29). It 
makes no difference whether the faces really meet or not; 
thus the angle MT is the inclination between the faces M 
and T, w T hich do not actually meet. The edge which would 
have been formed between these two faces is replaced by 
the face n. It may also be said that the edge M T is 
truncated by the face n. 

The interfacial angle is measured by means of the goni- 
ometer (see 36). Be careful to hold the goniometer at 
right angles to the edge to be measured ; otherwise the 
angle subtended will, of course, be found too small. If 
the crystal is held up towards the light, so that the edge 
appears as a point, the goniometer will be accurately ap- 
plied if held at right angles to the edge, and if no light 
passes between the crystal faces and the goniometer arms. 

171. By means of Ilaidinger's Method, the interfacial 
angle of even small crystals can be quite accurately meas- 
ured. Haidinger's goniometer consists simply of a glass 
plate, about SO mm. long, 25 mm. wide, and 1 mm. thick. 
One edge of this plate is ground off straight, so as to serve 
as ruler. Common window glass will answer. 



Crystallography . 9 1 



The mode of using this goniometer is described below.* 
172. The appearance of crystals of the same substance 
varies somewhat with the circumstances under which the 
crystals grew. Thus blue vitriol crystals are equally well 
developed on all sides if they formed on a fine string, but 
quite flat or tabular if they, during the growth, rested upon 
the bottom of the vessel containing the solution. Alum 
crystals appear as three or six-sided tablets (fig. 39) when 
grown on the bottom, but as double four-sided pyramids 



*The edge, such as A D in fig. 29, wherein the two faces M and Tmeet, whose inter- 
facial angle is to be measured, must be placed vertical to the glass plate. By means 
of a very little bee's wax, softened by pressure between the fingers, the crystal is 
held in the proper position on the plate. 

The beginner will easiest bring the edge vertical by means of the drawing square 
applied to the two sides M and T and the plate. For : in order that the edge A D can 
be vertical to the glass plate, both M and T must be vertical to the same plate. 

On a piece of card-paper (or on the common unruled writing paper of your journal) 
a sharp, straight line L L' (fig. 30) is drawn (best with India ink and a drawing pen). A 
short and fine line m m' is marked across L L', and obliquely downwards, to indi- 
cate that the crystal is to be placed below L L' and to the left of mm 7 ; the right 
extreme edge of. the crystal or body being exactly above m. 

Pl.icing the glass plate in this manner, wiih the crystal in the angle L m m', the 
plate is turned until one of the faces M, of the body is exactly in line with the line L 
I/. Then a. fine pencil line is drawn along the ground edge of the glass plate, say 
along R S ; mark it M on the paper. If need be, this side of the ruler may be marked 
by a bit of paper pasted near it ; for all the other lines must be drawn along one and 
the same side of the glass ruler. 

The plate is now turned until the other face T of the body has come in line with 
L L', over m, as indicated by the dotted line in the figure. A fine pencil line is 
again drawn along the same edge RS, and marked T on the paper, because corres- 
ponding to the face T. 

The angle between these two lines, marked M and Ton the paper, is now equal to 
the angle between the faces M and T of the body: provided the plane of the paper, 
or the plane of the glass, was at right angles to the edge. For the crystal and glass 
plate have been turned as one body; but the costal was turned the angle MT; 
hence the plate was turned as much, or the angle between R S (marked M) and R'S' 
)marked T) on the drawing is exactly equal to the interfacial angle MT of the 
crystal. 

By means of a horn protractor, this angle may be measured and expressed in 
degrees, in the usual manner. 

You continue this operation until you have measured the interfacial angles of all 
faces which are at right angl s to the glass plate; hence, in the above case, you will 
measure not only MT, but also TI, and M T and TM. Since opposite angles 
should be equal (M T = 31 7, etc.), you have herein a means to ascertain the degree 
of accuracy of your work. Accordingly, you can measure nil the angles in one zone 
by one adjustment. Thus, if a crystal of blue vitriol, figure 29. has been adjusted 
on the glass plate for faces M and T, it will be adjustpd for the entire zone M n T r 
M n Rr, and all the interfacial angles of this zone can be measured by simply turn- 
ing the glass plate, as described. 



92 Chapter ILL 



(fig. 37, 38,) when grown in the middle of the solution, on 
a string. 

This varying appearance of the crystals is termed their 
habitus. If the crystal is described and figured, the habitus 
may simplest be described by stating which face or faces 
dominate. 

173. But if the interfacial angles are carefully meas- 
ured, it is found that they remain the same between the 
same faces of the same substance, notwithstanding their 
changing habitus. This fact was first discovered by Steno, 
1669, and is often called Stenc?s Law of the Constancy of 
the Interfacial Angles of Crystals. It is the fundamental 
law of crystallography. 

Of course the facial angles are 'equally constant; but 
the interfacial angles, being more readily measured, we 
usually refer rather to these. 

We shall not here specially verify this law, because it is 
verified by the student's comparison of actual crystals with 
the description given in the subsequent. 

174. The following order should be observed by the 
student in this work of verification and identification of the 
crystal descriptions given further on : — 

Having received a crystal (from the teacher), turn to 
its description in this book. Study that description care- 
fully, comparing the crystal thereto. By this means you 
will soon be able to place the crystal in position* in ac- 
cordance with that adopted here, so that you can identify 
the faces on the crystal with those lettered in the figure. 

175. Next turn to your journal. Enter the name of 
the crystal, as given to you. Draw & figure of the crystal 
in the journal, representing the crystal as seen from the 
right and above. All peculiarities of the crystal should 
be faithfully delineated on the figure ; hence do not make 

*And mount the same on a pin, if not yet done. Handle these crystals with care, 
and return the same to the teacher when you are done. Only the best crystals are 
selected for this work. 



Crystallography. 93 



the figure too small, rather on scale 2 J 1 or 4 / t . Letter the 
faces on the figure in accordance with the figure given in 
the book. 

176. Measure the most important angles by means of 
the application goniometer (170) ; enter the result of your 
measurement in your journal. 

It is well, also, to measure one or several zones by means 
of Haidinger's method (171). 

Always compare your measurements with those given in 
the following descriptions. Tou may distinguish your ob„ 
served values as observed, from those here given, under 
the proper name of their observer. The angles on blue 
vitriol here given were observed by Kuppfer ; hence for 
this substance the headings in your journal will be : — 

Angle. Observed. Kuppfer. Error. 

MT. | 124°. ~\ 1^6° 10'. ~W. 

Etc. 

The error you had better always give in minutes. Never 
doctor your own observations, but enter them in the journal 
exactly as you find them by your observation. 

Also mark, in front of the first, or back of the last column, 
the goniometer used by you — either the Application Goni. 
ometer (170) or Haidinger's Goniometer (171). 

The following will now guide the student's work ; these 
descriptions are, of course, as terse as possible : — 

177. Blue Vitriol. Figure 29. — Habitus mostly tab- 
ular, M. Zone MT dominant, and all its faces usually 
striated parallel to the edge of this zone.* The oblique 
base P dominates over all other faces not yet mentioned^ 
and often occurs alone, bounding the zone MT. 

Primitive : MT 123° 10'— PT 127° 40'— MP 1 09° 15'. 
Zone MT: nr 100° 41'— Mr 126° 40'— Tr 110° 10'— 
Tn 148° 47'. 



*This forms a very good guide to bring the crystal in position. These striae are 
absent, however, on the best possible crystals. 



94 Chapter III. 



ZonerxP: Pr 103° 27'. 
ZonenP: Pn 120° 50'. 

Kuppfer, Observer. 

178- Hydrated Ammonio-Ferrous Sulphate. Figure 
31. — Habitus very variable ; crystals often quite distorted, 
especially if one of the faces MM' dominates. The oblique 
base P is usually striated parallel to edge Pq ; this fact, 
together with the triangular form of faces q, aids much to 
bring the given crystal in position. 

Primitive MM' about 109°, and MP=MT about 105°. 

179. Potassium Chlorate. — Habitus tabular; plates 
often very thin. Primitive PMM', with prism MM' 104° 
22'. The other angle PM=PM' 105° 35' cannot be meas- 
ured easily. 

180. Sucrose.* Figure 32. — Habitus often tabular 
P; or prismatic, if Par dominant. 

Primitive : MM' (on a) 78° 30'— MP—MT 98° 30'. 
Zone Pa r : Pa 103° 17'— ar 115° 33'— rP 140° 43'. 

Bammelsberg, Observer. 

181. Potassium NiTRATE.f Figure 33. — Habitus pris- 
matic; zone Mb dominant; often tabular, b ; usually only 
one of the domes DD' and dd' present. 

Zone Mb : MM' 119° 24'— Mb 120° 18'. 
Zone Ddb : bD 125° 6'— bd 144° 34'— Dd 160° 44'— 
DD' 109° <i8'— dd' 70* 52'. 

Rammelsberg, Observer. 

182. Potassium Sulphate. Figure 34. — Habitus, of 
the larger crystals (in drugstores), pyramid pr dominant; 
prism Mb short. The beautiful and brilliant crystals ob- 
tained from small quantities of solution are tabular, the 
zone Pb being very much lengthened in the direction of 
of the edge br, so that P is quite narrow, while b and r 
dominate. 

• *Crystals from common rock candy answer best. Small crystals in several varie- 
ties of common crystallized sugar; require magnifier. 
fCrystals best obtained in drug stores, among the common, pure Nitre. 



Crystallography. 95 

Zone Mb : MM' 120° 24'— Mb 119° 48'. 
Zone Pb : Pb 90°— rb 146° 11'— Pr 123° 49'. 
Pyramids : Pp 123° 40'— Mp 146° 20'— pp' 131° 8'. 

Mitscherlich, Observer. 

183. Potassium Chromate. — Very nearly the same 
form as potassium sulphate ; viz : — 

Zone Mb : MM' 120° 41'— Mb 119° 40'. 
Zone Pb : Pb 90°— rb 145° 35'— Pr 124° 25'. 

Mitscherlich, Observer. 

Hence potassium chromate is said to be isomorphom with 
potassium sulphate. Compare 182. 

184. White Vitriol.*— Habitus prismatic MM' 91 ° T 5 
the terminal four-sided pyramid p forms Mp 128° 58'. 

Brooke, Observer. 

Often only the alternate faces of the pyramid exist. 
Such crystals are called hemihedral. 

185. Epsom Salt. — Isomorphous with white vitriol; 
for MM' 90° 38\ Mohs, Observer. 

186. Sodium Nitrate. Figure 35. — Habitus often tab- 
ular, P; but the inclinations PF=PP"=PT" 106° 30' 
(Brooke) ; hence the form called a rhombohedron of 100° 
30'. Measure the three zones. 

187. Hydrated Potassium Cyanoferrate. Figure 
36. — Habitus tabular after the horizontal base; one of the 
pyramids (upper) usually dominates over the other (lower). 
M usually absent; if present, MM' 90° 55'. 

Zone Pm : Pm 111° 34'— mm' 136° 53'. 

Zone Pe : Pe 111° 51'— ee' 136° 19'. 

Wyrouboff, Observer. 

188- Sodium Chloride. — The primitive formed has 
PM=PT=MT=90°, or is a cube or hexahedron. These 
cubes are often united to hopper-shaped aggregations. 

♦Crystals must be kept in sealed glass tubes ; otherwise they become opaque and 
soon crumble from loss of water (effloresce). 



96 Chapter III. 



189. Potassium Bromide is isomorphous with sodium 
chloride. Large cubes can be had in any drug store. 

190. Alum. Figures 37, 38, 39. — When slowly grown 
in the middle of the solution (upon a fiue string) the hab- 
itus is octahedral, as represented in figure 37 ; when, how- 
ever, grown upon the bottom of the vessel, the habitus is 
tabular, as shown in fig. 39. 

The octahedron (fig. 37) is a double four-sided pyramid, 
bounded by eight equal and equilateral triangles, o. The 
interfacial angle between adjacent faces oo' is 109° 28', and, 
therefore, between opposite faces oo'" is 70° 32'. The octa- 
hedron has six equal four-sided corners, and twelve equal 
edges. 

If the octahedral alum crystal has attained 5 to 10 mm. 
in diameter, it usually exhibits the corners, and often also 
the edges replaced (see 170) by finely reflecting facets, as 
shown in figure 38. The facets h continued would consti- 
tute a hexahedron (188), while the facets d, replacing the 
twelve equal edges, would, sufficiently produced, constitute 
a dodecahedron. 

Hence the alum crystal, fig. 38, is a combination of the 
octahedron o, with the hexahedron h, and dodecahedron d. 
You will find : — 

hh 90° 0' oo 109° 28' dd 120° 0' 

ho 125° 16' hd 135° 0' od 144° 44' 

191. If iiow the crystal grows while resting on the bot- 
tom of a vessel, it becomes of tabular habitus after one of 
the faces o, and appears like fig. 39, on which you, how- 
ever, readily can distinguish and identify all the faces, h, 
o, and d. The facets d are usually rectangular, while h 
are octagonal and o hexagonal. In doubtful cases you 
need only to measure a few interfacial angles and compare 
the values with those given above. 

This study of the crystals of alum constitutes a most ex- 
cellent demonstration of the law of Steno, 173. 



Crystallography. 97 

192. Lead Nitrate. — Beautiful octahedra (o) with 
dodecahedral (d) and hexahedral (h) facets, but usually of 
of tabular form after o, are readily obtained. Transparent 
crystals* reflect and refract the light like diamonds. 

Lead nitrate is thus isomorphous with alum; Barium 
Nitrate also (183). 

193. The descriptions just given should also be used 
while studying crystallizations under the microscope (see 
161) — a study which is as charming as it is simple and 
easy. 

194. Besides the isomorphous substances described in 
180, 185, 188, 192, we must here mention two very inter- 
esting groups of isomorphous double sulphates, of which 
the types have been described in 190 and 178. 

Alum (190) may be obtained by mixing solutions of 
potassium sulphate and aluminium sulphate. The alum 
crystals also contain water.f Hence Alum is Hydrated 
Potassio- Aluminium Sulphate. Instead of Potassium Sul- 
phate we can take Ammonium Sulphate, and instead of 
Aluminium Sulphate we can take Ferric Sulphate or Chro- 
mium Sulphate — and still obtain octahedral crystals 
isomorphous with those of common alum. Hence the 
group of isomorphous alums may be represented as — 

i Potassio ] ( Aluminium ) 
> — < Chromium V — Sulphate 
Ammonio ) ( Ferric ) 
where any one, or even all, may enter in the same crystal. 
Those containing aluminium are colorless (or white when 
opaque) ; containing iron, the alums are pale, yellowish 
pink, and, containing chromium, they are of a rich, deep, 
blood-red color. Since in Alum all the zones are of equal 
angles, of course all alums agree exactly, and not only 
nearly, in their angles. See 183. 

*To obtain transparent crystals, the solution must be acid, and crystallize very 
slowly. 

fEasily proved by heating a small fragment in a narrow glass tube. 

13 



98 



Chapter III. 



Hydrated- j Ammonio [ — 



- — Sulphate. 



195. The crystal, fig. 31, described in 178 is also but 
one of a large number, which may be obtained by mixing 
any two of the sulphates, as indicated in the following gen- 
eral formula : — 

" Magnesium " 

Zinc 

Cadmium 

Manganese 

Iron 

Nickel 

Cobalt 

Copper 

Since these crystals have been very carefully studied by 
Carl von Hauer, we term them Haueroids. They are ex- 
ceedingly beautiful* not only in form, but also in color. 
Those containing Magnesium, Zinc, Cadmium, are color- 
less (white when opaque) ; containing Manganese, they 
are pale pink; with Iron, pale green ; with Nickel, deep 
apple green ; with Cobalt, brownish pink ; and with Cop- 
per, blue. 

The Haueroids are all isomorphous (183), having nearly 
the same angles. The Haueroids containing Ammonium 
have the following interfacial angle of the primitive prism 

MM': — 

mm'. 

Magnesium 109° 30 

Zinc... 111°0' 

Cadmium 109° 24' 



Manganese 



Iron 



Nickel 109° 20' 

Cobalt 109° 28' 

Copper 108° 56' 

The total range is, thus, only 2° 4'. 
196. By placing a less soluble Haueroid into the solu- 
tion of a more soluble one, the latter grows over the former, 
and forms beautiful double crystals, especially if of differ- 



Crystallography. 99 



ent colors. Such crystallizations are termed episomorphous. 
A green potassio-nickel Haueroid may thus be surrounded 
by a red band of the ammonio-cobalt Haueroid, and finally 
by a vj/iite belt of the ainmonio-zinc Haueroid. 

197. It has already been stated (147) that crystals and 
crystallized bodies break with more or less readiness in cer- 
tain directions forming smooth, plane surfaces, termed cleav- 
age planes. These cleavage planes are always parallel to 
some of the prominent crystal faces. 

This property may be readily studied by means of small 
crystal fragments (2-5 mm. in dimension) ; the cleavage 
may be produced by means of a pen-knife pressing the sub- 
stance while supported on white paper. 

198. The crystals described in the preceding wiil thus 
be found to possess the following cleavage in direction and 
degree :-— 

Blue Vitriol (177), P and T, very imperfect. 

Hydr. Am. Fer. Sulph. (17S), none. 

Potass. Chlorate (179), P, M, M', highly perfect. 

Sucrose (180), a distinct. 

Potass. Nitrate (181), M, M', b, imperfect. 

Potass. Sulphate (182), P, b, imperfect. 

Potass. Chromate (183). 

White Vitriol (184), b. 

Epsom Salt (185), b perfect; 2 at right angles to b, and 
under 120° 4'. 

Sodium Nitrate (186), P,P',P", highly perfect. 

Potass. Cyanoferrate (187), P, very perfect ; lamellar. 

Sodium Chloride (188), 3 perfect cleavages at 90 Q . 

Potass. Bromide (189), ditto. 

Alum (190), no cleavage. 

Lead Nitrate (192), no cleavage. 

Haueroids (195), no cleavage. 

The faces of cleavage indicated by these letters will, by 
the descriptions referred to, readily give the angles formed 
by these cleavage planes. 



100 



Chapter III. 



199. A line drawn through the crystal parallel to the 
common direction of the edges of a zone, is called the axis 
of that zone. Each zone contains at least two different 
faces, MT and their parallel MT (compare 167, 168, and 
169). A plane at right angles to this zone will intersect 
it, so that the section formed* is a rhomboid, if the adja- 
cent sides are of unequal length, and a rhombus if they are 
of equal length. If the angle MT is 90 Q , this rhombus be- 
comes a square {quadrat) ; if 120°, the zone always has one 
additional pair of faces, so as to make the section a regular 
hexagon. 

Since one zone cannot bound a crystal, it cannot either 
fully characterize the same. Hence any two of the above 
sections will suffice to characterize the crystal. All crys- 
tals having sections of the like name are said to crystallize 
in the same system. 

On this characteristic of crystals the following nomen 
clature is based : — ' 





FIRST SECTION. 


SECOND SECTION. 


NAME OF CRYSTAL 
SYSTEM. 


H 
■ 
§ 

s 

CO 


1 


Rhomboid 

Rhomboid 

Rhombus 

Rhombus 

Rhombus 

Square 


Rhomboid 

Rhombus 

Rhombus 

Square 


Triclinic 


?, 


2 




4 


3 
4 
5 


Rhombic 

Quadratic 

Hexagonal 

Tesseral 


8 

16 

94 


6 


Hexagon 


48 











The figure under " Symmetry " gives the maximum 
number of like faces in any form. The crystals described 
or mentioned are : — 



♦If the zone is measured by Haidinger's Method (171), this section is obtained as 
the drawing. Only bear in mind that the linear dimensions are arbitrary on crystals 
(173), so that in this drawing you may move any line parallel to itself (53). The best 
way to represent this independence of the linear dimension is to move each one oj 
the lines until, parallel to itself, it exactly touches a circle drawn anywhere in the 
figure ; then all lines are equally distant from the center of that circle. 

Two diagonals of this section may now be constructed, and used as the second and 
third axis together with the axis of the zone as the first or vertical axis. 



Crystallography . 101 



Artificial: Native (165): 

Triclinic: 177 Nos. 24, 25. 

Monoclinic : 178, 179, 180, and 195 " 21-23. 

Kkombic : 181, 182, 183, 184, 185 " 9-14. 

Hexagonal: 186 " 15-19. 

Quadratic : 187 (nearly quadratic) " 6-8. 

Tesseral : 188, 189, 190, 191, 192, 194. . . " 1-5. 

Notice how nearly hexagonal the monoclinic (179), and 
the rhombic (181, 182, 183) ; also how nearly quadratic the 
rhombic (184 and 185). 

200. From what has been shown, it is apparent that 
the crystal form of substance is a fundamental property of 
matter, almost as general as magnitude and weight, but 
more specific. Indeed, substances may readily be distin- 
guished by this property, either by simple aspect (sodium 
nitrate, 183, and potassium nitrate, 181), or by more care- 
ful measurement. Any adulteration by the former can 
thus most readily be detected (184 and 185). 

The process of crystallization is also extensively applied 
in the chemical arts for the purification of substances. 

But the study of crystal form is above all of highest 
theoretical importance, because it necessarily leads towards 
the elucidation of the mysteries of the true nature of mat- 
ter. 



CHAPTER IV. 



ON LIGHT AND VISION. 



I. Lustre and Color. 

201. We see bodies at a distance from us by the 
light which they send into our eye, the special organ of 
vision.* The branch of physics, treating of light, is often 
called Optics. 

202. By this organ and through the agency of light, 
we obtain knowledge not only of the objects on our earth 
beyond the reach of our hand, but also of the heavenly 
bodies far away from the earth ; the Sun, the Moon, and 
the Stars** 

203. A body is said to be luminous (or self-luminous) 
if it produces the light it sends forth. 

A body not luminous can only be seen when exposed 
to the light of some luminous body ; that is, when the body 
is illuminated. When not illuminated, non-luminous 
bodies are dark. 

204. The sun is the principal and brightest luminous 
body of our world. Flames of various kinds f are also 
luminous, and constitute the principal artificial sources of 
light. 

205. An illuminated body is either opaque, translucent, 
transparent, according as it transmits no light, very little 
or most of the light falling upon it. The illuminated 
opaque bodies throw a shadow behind them. 

♦Any attempt to define these words is preposterous ; no one blind-born would 
understand the words defined. 

♦♦These objects will be studied in the third volume, on Cosmos. 

fCandles of tallow or stearine; lamps filled with fat oils or coal oils (kerosene); 
illuminating gas. 



Color and Lustre. 103 



206- We may also say that a body is transparent if 
we can recognize the form of objects by looking through 
the same. If only a dim light shines through the body, 
this latter is translucent ; often only on its edges. If no 
light at all passes through the body, we call it opaque. 
Examples: glass-plate, horn-sheet, metal-plate. 

207. All bodies show n°>t only their form when illu- 
minated, but also a peculiar reflex or lustre and a peculiar 
shade of color. 

208. Of lustres we distinguish especially the metallic 
and vitreous (glassy) lustre ; also, silky , pearly, resinous 
lustre. As typical examples notice the reflex of lead (a 
fresh cut surface), glass, silk, pearl, resin — all kept per- 
fectly clean. 

A body reflecting much light but having no real metal- 
lic lustre, is often said to possess a sub-metallic lustre. If 
the body possesses no peculiar lustre, it is said to be dull 
and earthy. 

209. It will be found that only opaque bodies have 
metallic lustre, and only transparent bodies have vitreous 
lustre. Translucent bodies have pearly, silky, or resinous 
lustre. 

210* Of colors we distinguish* the mixed colors, 
white and black, with the various intermediate degrees of 
grey; and the pure colors, red, orange, yellow, green, blue, 
violet, purple, in many different shades. The intermediate 
shades are called greenish yellow, yellowish green, etc. 
Intermediate between the pure and the mixed colors are : 
brown, buff, umbra, etc., etc. 

At times the color in reflected light differs from the 
color shown in reflected light. Example: thin gold leaf! 

211. The student should carefully recognize all these 
optical properties of the bodies before him. For practice, 
he should, in his journal, describe the optical properties of 

*Some persons cannot distinguish red from green or blue from black, etc. Such 
persons are said to be color-blind. 



104 Chapter IV. 



at least ten of the crystallized substances enumerated in 
155. The well crystallized substance should be kept in 
small, labelled specimen tubes. To find the streak (149) a 
portion of less perfect crystals should be kept in another 
tube, and a very small quantity thereof should be crushed 
by a pen-knife blade at the spot in the journal where the 
result is to be recorded. 

212. The so-called chemical elements, especially some 
of the more common metals, (gold silver, mercury), copper, 
lead, etc., and the metallaids, sulphur, carbon and iodine, 
should be described in like manner. 

213. The same observations should be made on as 
many as possible of the minerals enumerated in 165, or of 
others, which may be accessible. 

214. The physical characteristic of a substance con- 
sists essentially of its optical properties (213) which are 
noticed upon looking at the same, together with its 
morphological properties (crystal form and cleavage, see 
174 to 176 and 197) observed upon closer inspection, and 
by the division of the substance ; to these must be added 
the hardness'H (see 150) and the specific gravity 6 (see 30 
and 123). Also the molar properties, fracture, malleabil- 
ity, or brittleness, (147) and flexibility or elasticity (146). 

215. The order in which these properties are ascer- 
tained is as above given, namely, optical, morphological, 
hardness, specific gravity, and the molar properties. 

If this work is faithfully and carefully performed, the 
student will have made considerable progress in the art of 
observation; he will have begun to see. 

216. The results observed should invariably be re- 
corded in the journal, in the following order: — 

Number. Name. 

Opacity 

Lustre 

Color 

Streak 

Crystal Form 

Cleavage 

Hardness, H— 

Specific Gravity, G = 

Molar Properties 



Spectrum and Prism. 105 

II. THE PRISM AND THE SPECTRUM. 

217. A glass rod dipped into water (contained in a 
porcelain dish or beaker) appears as if broken at the sur- 
face of the water. This phenomenon is due to the refrac- 
tion of light at the surface between two transparent bodies 
— here water and air. 

218. By refraction objects appear slightly displaced 
when seen through thick plate-glass, the sides of which are 
parallel. 

219. If the two surfaces of a piece of glass are not 
parallel, the piece of glass is called a prism. Objects seen 
through a prism are very much displaced by refraction. At 
the same time their outline is more or less vividly colored. 

220. To observe these colors plainly, look through a 
prism P at a narrow strip S of white paper (about 4 mm 
wide and 100 mm long) in the manner shown in Fig. 40. 
The eye at E will then observe a band r of beautiful red 
nearest the strip S ; closely to the red follow successively 
orange, yellow, green, Hue, (indigo,)* violet. The colored 
band ot seven colors is the spectrum.\ 

The strip of white paper should rest upon a piece of 
black cloth, destitute of lustre. 

221. The colors are evidently thus spread or dispersed 
because they are not equally refracted ; the phenomenon 
is termed the dispersion of light. 

222. These seven colors represent a great multitude of 
slightly different shades of color, which all are in the white 
light reflected from the paper. Hence the white light 
consists of these colors, and the prism analyzes that light, 
showing what colors white consists of. 

223. Cover one pane of the window with a piece of 
zinc having a narrow slit about 2 mm. wide by 100 mm. 
long, and now observe the bright daylight of the sky pass- 

*Indigo is simply a dark blue, and hence by many authors is not counted as a dis- 
net color. 
fAlso observed in the rainbow. 

14 



106 Chapter IV. 



ing through this slit, by means of the prism held at the 
distance of two or three meters. You will then see a 
spectrum of still more brilliant colors, but in the same 
order. This spectrum is called the solar spectrum because 
it results from the analysis of the diffuse sunlight. 

224. You can now more carefully analyze the color of 
solids and liquids. The solids are placed in line with, the 
paper strip on the black cloth (220). The liquids are sup- 
ported closely in front of the slit (223). 

225. The spectra thus observed are not complete ; 
certain parts therein remain dark ; they are termed 
absorption spectra. For the same substance the absorption 
spectrum is nearly always the same — so that substances 
may be identified by means of the absorption spectra they 
give. Upon these facts the celebrated spectrum-analysis 
is based." 

226. The observations — which must be made with 
much care and patience, not hastily — are recorded in the 
following manner in the journal : 

Number | Name of Substance || r | o | y | gr | bl | i | v. 

A star or cross is marked in the column of the colors 
observed ; r stands for red, etc. Blue vitriol and potas- 
sium bichromate are excellent examples, both as solids and 
in solution. 

227- If the spectrum colors (222) are all united again, 
white results. This has been proved in various ways, 
which it is not necessary here to describe. 

If only part of the colors of the spectrum are united, 
a mixed color A results. If the remaining colors are also 
separately united, another mixed color B will result. If 
now these two again are united, white must result, 
because then all the colors of the spectrum will have been 
united. 

Any two shades of color which together produce the 
impression of white, are said to be complementary colors. 

♦Treated of in Vol. II. 



Spectrum and Prism. 107 

228. Approximate experiments on the compound and 
on complementary colors may be performed by the follow- 
ing simple apparatus : — 

To a string — best a thin catgut string — a lead weight 
of 20 to 50 grammes is suspended. A disk of paper, W to 
15 centimeters in diameter, is put with a small central slit 
on the hook of the weight, and then the string is attached 
to the hook, while the other end of the string (about 30 to 
40 centimeters long) is rapidly twirled between the thumb 
and the first finger of the left and right hands ; then the 
disk will soon rotate in a horizontal plane with great rap- 
idity, while the weight holds the string vertical. 

If now the outer rim of the disk has been colored alter- 
nately blue and yellow to about two cm. from the cir- 
cumference, it will appear green during the rotation. 
Hence green results from blue and yellow. 

229. In this manner experiment with some of the fol- 
lowing colored disks, and record the result in your journal, 
thus : — 

Number. Colors on disk. Resulting colors. 

The following are some of the most important examples : 
Blue and yellow; green and yellow; green and red; yel- 
low and red; yellow and violet; orange and blue; red 
and blue. 

Whenever the color observed is whitish grey, the cor- 
responding purer colors would have yielded a white tint; 
the colors taken are therefore nearly complementary. 

230. It is often of some practical importance to bear 
in mind that colors placed near each other appear modi- 
fied as if each one had been mixed with a portion of the 
other. 

For this study, have some squares (about one dm. side) 
of colored paper. For example, to determine the effect 
of the association of blue and yellow, have two such 
squares of each color, and have pasted on one of the blue 



108 Chapter IV. 



a smaller square of yellow, and on one of the yellow a 
smaller square of blue. You will notice the blue on the 
double card will appear purplish, while the yellow will 
6how a turn of orange. Record your observations ! 

231- The flame of an alcohol lamp or a Bunsen gas- 
burner* is nearly colorless, and but very faintly luminous. 
If a drop of a strong solution of common salt is held into 
such a flame by means of a small loop of platinum wire, 
the flame becomes very luminous, and exhibits a bright 
yellow color (with faint orange tint). By means of other 
solutions other colored flames can be obtained. 

232. If a small strip of thin copper sheet is held in 
the flames, the latter exhibits a beautiful green color. The 
copper, however, must from time to time be freed from 
the black crust forming thereon. This is best done by 
dipping the copper into nitric acid ; the strip may then 
immediately be reintroduced into the flame. 

233. This green flame is called the copper flame. So 
also the yellow flame (231) is termed the sodium flame, 
because common salt contains the metal sodium. 

234. In a dark room — or a properly darkened case 
— carefully observe the color of various substancesf when 
illuminated by the sodium flame. Also observe the color 
of a. strip of white card paper, on which a spectrum has 
been painted, or on which pieces of paper of various col- 
ors have been pasted. Record your observations in the 
journal, thus : — 

Observed Color. 



•^ I Name and description 
of object. 



Daylight 



Sodium flame. 



235. These results are easily explained. The daylight 
contains all the colors of the spectrum (230) ; of these, the 

♦Both fully described in vol. II. 

fEspecially striking are the results with potassium bichromate, and mercuric 
iodide, blue vitriol. 



Lens and Image. 109 



object only reflects certain ones (224, 225). If only yel- 
low light illuminates the object, only this can be reflected. 
Hence only this color will remain in the the body, if yel- 
low is among the colors which it reflects. 

236- Results similar, but not so striking, are familiar 
to everybody ; for all know, that colors look differently at 
gas or candle light than in the broad daylight. Certain 
shades of purple appear almost black at gas light, etc., etc. 

237* Light not only informs us, through our eye, of 
the existence, form, and magnitude of external objects of 
the world at large, but varies this perception most admir- 
ably by lustre and color. Enumerate the colors observed 
in the world around you, in sea, mountain, forest, etc., etc. 

238- The color observed on objects depends, however, 
first, upon their specific nature, (224) ; secondly, upon the 
light shining upon them (234), and lastly, upon the eye 
observing it, (210, note). How would our meadows and 
forests appear if the sunlight was not white, but pure yel- 
low, like the sodium flame ? What color would the human 
countenance exhibit ? 

III. THE LENS AND OPTICAL IMAGES. 

239. A lens is a thin, round disk, of perfectly clear 
glass, bounded by two spherical surfaces. In some lenses 
one of these surfaces is plane.* 

240. The principal forms are the double convexlens, A, 
and the double concave lens, D, of which figure 41 shows 
a transverse section. The plano-convex B and themensi- 
cus C, act upon light like A, for they are thicker in! the 
middle than in the margin ; they are often termed convex 
lenses. The plano-concave E, and the concave-convex F, 
resemble D, in their effect upon light ; these three are best 
considered as concave lenses. 

241. All convex lenses have a {principal) focus f F, 
wherein all parallel rays striking the lens meet one an- 
other after having passed through the lens. 

*This corresponds to a sphere of infinite radius. 



110 Chapter IV. 



Hold the convex lens L in the sunlight, its face at right 
angles to the sun's rays, S, as shown in fig. 42; the focus 
F, then will readily be found by moving a piece of brown- 
ish or whiteish paper held parallel to the lens from this lat- 
ter outward toward F. On this paper you will see a circle 
of light, which circle diminishes as you move the paper 
from the lens. At the focus F the circle is smallest 
and brigldest / here you have in fact a small image of the 
sun, all the light striking the lens is here concentrated ; 
also all the heat, so that the lens can be used as burning 
glass. 

If you remove the paper further from L than F, the 
circle becomes larger again. 

242- The focal length f of a lens is the distance from 
its principal focus F to the centre^of the lens L. — Careful- 
ly determine the focal length of a few given lenses (in cm 
and tenths thereof). Record the result in your journal, 
thus ; — 
Number. j Description of lens. Focal length. 

243. Image of a distant object. — Hold the face of a 
lens toward a distant object, such as a house, a church etc. 
Behind the lens, and parallel to its face, move a piece of 
white card paper, slowly from the lens as in 241. First 
you will notice but a white disk of light, but when you 
have reached the distance of the principal focus you will 
already recognize the outline of an inverted image of the 
object on the card ; if you now continue to remove the 
card, but very gradually, the image will become more and 
more distinct. At a certain distance it is most distinct ; 
tills distance is called the distance of the image and will 
be denoted by i. As stated above, for a distant object, i 
is greater than f ; and you will soon find that the nearer 
the object, the more i exceeds f. 

Beyond the distance i, the image again becomes indis- 
tinct. Hence at i the object is said to be in focus. 



Lens and Image. Ill 



The image is seen to be real, inverted, and diminished 
in regard to the object. 

244. Make a series of experiments with a lens. First 
determine the focal length f (24:2) ; or, if the weather does 
not permit, have the focal length stated to you by your 
teacher. Then observe the image of several objects* 
always carefully measuring the distance i of the image 
from the middle of the lens. You may also enter the esti- 
mated distance o of the object. Record in your journal, 
thus : — 

Description of lens ; its mounting, etc. 

f= 

Number. Object, and its estimated distance o. i, 

245- The camera obscura used by photographers, consists 
essentially of a convex lens. To make the image easier 
observed, all light but that from the object is carefully 
excluded by means of a box blackened on the inside, and 
heavy black velvet to envelop the head of the obscura. 
The use of this camera is well known. 

246- The Eye of all vertebrates is also essentially such 
a camera. The observer is represented by the numerous 
nervous fibres covering the interior of this camera, and 
running to the brain. 

All objects we see are thus most delicately and ex- 
quisitely pictured in our very eye. 

247. The direction in whicn the light passes through 
a lens cannot be of any influence on the resulting refrac- 
tion. Hence, if the parallel rays of the sun, fig. 42, pass 
to the focus F and onward, it follows, that light radiating 
from the focus F will, after having passed through the 
lens, form parallel rays of light. So also in 243 ; if the 
object A at a distance o gives rise to a real, inverted, di- 
minished image JB at a distance i from the lens, an object 
B at the distance i would form an image identical with A 
at the distance o from the same lens. 



112 Chapter IV. 



These facts are usually expressed by saying that the 
object and image are conjugate in reference to the lens; 
that is, they may change places. 

248- To demonstrate this, place a burning candle A as 
the object, at a reasonable distance (2 to 3 meters) from a. 
tolerably large lens, on a table, in a dark room — or simply 
during a dark evening. Hold a small card at the precise 
place where the image B forms ; compare 243. INow re- 
place this card by a small burning taper; extinguish the 
flame of the candle A and hold a large white sheet of 
paper in its place. Tou will then notice the real, inverted^ 
and magnified image of the flame of the taper on this- 
paper. Here, evidently, object and image have changed 
place. 

249. If the object is nearer the lens than the principal 
focus, o < f ; or as we may express it, if the object is inside 
the focus, no real image can form ; for the rays will diverge 
after passing through the lens. Fig. 4.3. To an eye looking 
through the lens the rays seem to come from points fur- 
ther from the lens than the object. No real image is 
formed ; but the place where the object appears to be, is- 
termed the virtual image of the object. This virtual 
image is erect, and magnified. 

250. Hence a single lens constitutes a magnifying 
glass if we bring the eye close to the lens and the body to 
be examined a little inside the principal focus of the lens. 

251. For proper observation the virtual image should 
be at the distance of distinct vision, that is about 25 to 30 
cm. Since now the object has to be brought inside the 
focus, it will readily be seen that the glass will magnify 
the more the smaller its focal length is. But the smaller 
this focal length, the smaller will be the part of the object 
seen at once, and the more faint the image will be. 

252. This latter defect is remedied by taking several 
larger lenses of greater focal length, one before the other. 
Usually three different lenses, of slightly different focal 



Lens and Image. 113 



lengths or powers, are mounted together, so that accord- 
ing to the power required, either one, two, or all of them 
may be used. 

253- Determine the magnifying power of the glass by 
carefully observing how many millimeters at distance of 
distinct vision one millimeter under the glass does cover. 
Look with the right eye through the glass and with the 
left eye at the other millimeter scale. If the view be- 
comes indistinct close the left eye for a few moments. Ob- 
serve various objects through such magnifiers, and sketch 
what you observe in your journal ; adding the necessary 
explanations in words. 

Examples: The fingers ends ; a hair; small portions of 
pocket handkerchief ; paper; point of a needle; point of 
a pen ; edge of a good pen-knife, etc. Also, the crystals 
formed on glass-slips (116). 

A good magnifier is, in fact, constantly required by the 
close observer. 

254. Spectacles are lenses of small power or compara- 
tively great focal length. Far-sighted persons, who would 
have to hold the page they read at more than 30 cm re- 
quire convex glasses. Near sighted people demand con- 
cave glasses. Can you find out why ? 

255. The relation betioeen the distance o of the object 
and the distance i of the image for any convex lens of focal 
length f is : 

O 1 f 

If the lens be concave, the law is still applicable, only 
that f then is negative. 

256- This relation should be proved by carefully meas- 
uring f, o and i ; as object, the flame of a candle is very 
useful. The experiments may be performed any dark 
evening ; or during the day time, if a room, which can 
readily be darkened, is at hand. 

The results should be recorded in the journal, thus : — 

Series L Description of lens used. 
15 



114 



Chapter IV. 



No. 



Determination of f - Calc. j 

Observed, 
o I i 



Calculated. 
- I - 

o I i 



+ 1 



Here d is the difference between the two sides of the 
equation in 255. 

257- The construction of the image is also often of 
considerable interest. It may be done by using the fol- 
lowing facts : — 

1. A ray passing through the center of the lens, is not 
changed in directness; i. e., forms (practically) a straight 
line. 

2. A ray parallel to the axis* of the lens passes 
through the principal focus (see 241). 

Since any point is determined by the intersection of 
two lines, any point of the image will be determined 
by constructing the above rays for the corresponding point 
in the object. 

Example. — Focal length f = 2 cm. Distance of object 8 
cm ; the object is a straight line, one centimeter long, and 
at right angles to the axis of the lens. Find the image by 
construction ; also measure the distance of the image and 
the magnitude of the same. 

IV. THE TELESCOPE. 

258- The Telescope is an optical instrument through 
which distant objects can be distinctly seen as if they were 
much nearer by. 

Galileo invented the telescope 1610, and made most 
astonishing discoveries in the heavens by his instrument. 
His telescope is still in general use under the name of 
Opera glass. Kepler changed and simplified the instru- 
ment to what is now usually termed the Astronomical Tel- 
escope. A third kind is the terrestial telescope, or Spy 
Glass. We shall describe each kind. 

259. Kepler's 'Telescope or the Astronomical Telescope 
consists of two convex lenses. A larger lens turned toward 



♦The axis is here a line perpendicular to the lens at its center. 



The Telescope. 115 



the distant object, and therefore called the Object-lens, 
forms a real, inverted and diminished image of the object ; 
compare 243. This image is again carefully observed 
through the other and smaller convex lens held near the 
eye as a magnifier (see 249 to 253) ; this lens is called the 
Eye-Lens of the Telescope. The two lenses are supported 
by tubes blackened on the inside, and the tube is often 
properly mounted upon some support. 

260. The distance of the image from the object lens 
is greater for near objects than for objects farther off; (see 
244), always somewhat beyond the focal length F of the 
object-lens. To observe this image distinctly by the eye- 
lens magnifier, the latter must be brought somewhat 
nearer the image than its focal length f. Hence the dis- 
tance between the two lenses is nearly the sum of the 
focal lengths F and f of the lenses. 

261. To observe more or less distant objects equally 
well, the eye-lens must therefore be moved slightly from 
the object-lens for objects near by. This is usually done 
by sliding the tube holding the eye-lens in the tube which 
supports the object-lens. This is called to focus the object. 

262. To become thoroughly familiar with this most 
important instrument, experiment with two lenses, of 
about twenty and four centimeter focal length respectively. 
Place the first (the object-lens) at a distance of 3 — 4 
meters from a small card A, on which a few words have 
been written ; the card may be fastened to some wall or 
support, but must be sufficiently illuminated. On another 
small white card find the place of the image B of A (com- 
pare 243). Then place yourself with the magnifier or eye- 
glass in such a position that fine writing on the back of 
the card atB appears distinct and magnified; now remove 
that card and you will see the writing on card A distinctly 
and much magnified — but inverted. 

This experiment is very much facilitated if the lenses 
and the cards are mounted on proper supports. 



116 Chapter IV. 



Describe in your journal the results of your observa- 
tions, and the lenses and supports made use of. 

263. While looking through this telescope with the right 
eye, observe the card directly with the left eye. You will 
then see how much this simple telescope magnifies. If any 
of the two images in the two eyes becomes dim, just rest 
the corresponding eye a few seconds by simply closing the 
same ; upon reopening the eyelid you can continue the 
comparison in magnitude. (See 253.) 

264. By a little care you can make the lower edge of 
the card seen direct by the left and through the telescope 
by the right eye, coincide in level. Have some one of 
your colleagues move a ruler slowly upwards above the 
card, and tell him "stop" when this ruler is in level with 
the upper margin of the card as it appears through the 
telescope. Then measure the height H of this ruler above 
the lower edge of the card ; also, the height h of the card 
itself. Then: — 

m— 5 

h 

is evidently the magnifying power of the telescope. 

265. If you determine the focal lengths F and f, you 

will find that 

m' = F 
f 
is very nearly the same as the above m. 

266- From this it follows, that with the same object 
glass (F) you may use different eye-glasses (f) and thus 
secure a different degree of magnifying power. The 
smaller the eye-glass, or the shorter its focal length, the 
greater will evidently be the magnifying power of the 
telescope.* 

267- Good telescopes are therefore usually accom- 
panied with several eye-glasses, often spoken of as the 
different powers of the telescope. Thus the powers 15, 30, 

♦But at the same time the field of view seen at one time through the telescope 
will become smaller, and also the image less bright. 



The Telescope. 117 



etc., mean eye-glasses, which combined with the same 
object glass produce a magnifying power of 15, 30, etc. 

For reasons given in 252, these eye-glasses are often 
composed of two or more lenses, and are then more prop- 
erly called eye-pieces. 

268- If you observe carefully through the telescope 
described above (262) you will notice colors surrounding 
the letters and the margin of the card ; especially the col- 
ors blue and red. This is due to the dispersion produced 
by the lens, because each convex lens is like a prism of 
circular shape. See 219, 220. 

269. These colored fringes are avoided by also com- 
bining two lenses to an object piece / the resulting object 
piece and the entire telescope is said to be achromatic. 

Such a double lens consists of a double convex lens of 
crown glass and a double concave lens of flint glass ; the 
former is turned toward the object, the latter towards the 
eye-piece. 

The achromatic object glass costs usually at least as much 
as all the other parts of the telescope taken together — 
especially in the very large telescopes. An achromatic 
object piece, costing $10,000, is not so xerj large yet. 

270. The amount of light falling upon the object piece 
is not very much diminished in its course through the 
glasses, and finally enters the eye. When observing the 
same object with the naked eye, only a beam of light as 
large as the pupil of the eye is received. If therefore D 
is the diameter of the object piece, and d the diameter of 
the pupil, the illuminating power of the telescope is (48) 

The mean diameter of the pupil is about five millimeters. 
Hence if the object glass has a diameter of five centi- 
meters, the illuminating power of the telescope will be 
100. 



118 Chapter IV. 

271- The brightness of the image observed in the tel- 
escope depends upon the magnifying and the illuminating 
power. If the telescope magnifies 10 times, the size of 
the image is 10 2 or 100 times as large as the object ap- 
pears to the naked eye. If the illuminating power is also 
100, then the image is as bright as the object ; if it is less, 
then the image will be less bright. 

272. In general the brightness is b is the square of the 
magnifying power m divided by the illuminating power, or 

b = ™ 2 . 

i 

That is, by 270 and 265 : 

b = (I . i\ 2 
U d) 

273. From this it will appear, that for a given tele- 
scope high powers can only be used on bright objects; 
faint objects soon are so much magnified that they become 
almost invisible. 

It also is plain, that telescopes intended for the observa- 
tion of faint objects, should have very large object glasses. 
Such telescopes are the opera glasses and comet-seekers. 

274- The student may now use a good achromatic 
(269) telescope. Determine its magnifying power by th e 
method of 264 ; it will for more powerful instruments be 
well to place the object at a considerable distance. Also 
determine the illuminating power by 270. Hence the 
brightness by the first equation b. Record the results in 
the journal, together with a concise statement of what 
particular details you can distinguish on distant objects 
observed* by you. This exercise is both very useful and 
quite entertaining. A sketch should be added correctly 
representing the telescope used. 

275- You may also observe the moon — especially the 
crescent! Also the sun — but only through the sun-glass. 

*If the telescope is in a room, the window must be raised, because our window 
glass is so irregular and will totally destroy the outlines of the image. 



The Telescope. 119 



The teacher may give farther instructions ; but the ob- 
servations of the heavenly bodies through the telescope 
will be more fully treated of in vol. III. 

276. For many terrestial observations it is unpleasant 
to see everything upside down, as it appears in the tele- 
scope described. 

Hence, a so called terrestial eye-piece often accompan- 
ies the telescope. In this eye piece two or three more 
lenses have been added, so as to re-invert the image and 
thus make it erect. Of course much light is lost by passing 
through so many lenses. 

277. In Galileo's telescope the convex eye-glass is re- 
placed by a concave one. Thereby the image is also 
erected. Hence this telescope is still in general use as 
opera-glass. Only low powers can be used with it; but 
since the object lens of opera-glasses is usually very large, 
they have a great illuminating power and a high degree 
of brightness. 

Observe also with such a telescope as directed in 274. 

278- AH telescopes described thus far are known as 
Refractors, because the object piece is a lens, or a refractor. 

279- Formerly concave mirrors were much used in- 
stead of the object-lens. Those older telescopes were 
therefore called Reflectors. RersclieVs and Lord Ross's tele- 
scope, are huge reflectors of respectively 120 and 180 cen- 
timeters radius. 

280. Diffraction-Experiments. — In front of a bright- 
flame place a metallic screen with a small round hole. At 
a distance of several metres place the telescope, and focus 
the above hole, so that you see a small disk of bright light 
(using low powers.) 

Now cover the object-glass by means of a box of card 
board. In the bottom of this box a round or square hole 
of 1 or 2 cm. radius has been cut. This hole is, for differ- 
ent boxes, covered with thin silk ribbon or other wove; 
tin-foil with one, two or more fine holes carefully made 



120 Chapter IV. 



with the point of a sharp needle ; tin-foil with one or two 
or more parallel and fine knife-cuts ; tin foil with a small 
rhomb cut out, etc., etc. 

Describe and sketch in your Journal the beautiful phe~ 
nomena of diffraction which you will now observe through 
the telescope ! 

The cause of these phenomena is that light passes as it 
were to some extent around a corner and not exclusively 
in a straight line ! 

V. THE MICROSCOPE. 

281. The microscope is an optical instrument through 
which the details of minute objects can be distinctly seen 
as if they were many times larger than in reality. 

282. The microscope consists also (259) of an object piece 
and an eyepiece. The object piece is in every respect the 
conjugate of the object piece of the telescope, (compare 
247). The object is placed a little beyond the focus of the 
object-glass ; hence a real, inverted and magnified image 
is formed at a considerable distance beyond the focus on 
the other side. This image is again magnified by means 
of the eye piece, precisely as in the telescope. 

283. In the microscope, however, the object lens is the 
smaller, the eye-lens the larger. The object piece is usu- 
ally composed of several achromatic lenses, and the large 
instruments always are provided with several such object 
pieces of different powers. 

284. As for the telescope, so also here, the magnifying 
power cannot be indefinitely increased. The greater the 
power, the nearer the object piece has to be brought to the 
object. The lack of light is here easier overcome by plac- 
ing a concave mirror below the transparent object or aeon- 
vex lens above the opaque object observed. 

285. In working with such a microscope bear in mind 
that it inverts, exactly as the astromonical telescope. If 
you wish to move the particle observed to the right in the 
field of view, you must move the glass-slide on which the 
object rests to the left, etc. 



The Microscope. 121 



286. The magnifying power of a given microscope is 
easiest determined by carefully observing a fractional mil- 
limeter scale* through the same by the right eye, and 
copying the same in pencil on paper by aid of the left eye, 
always aiming to have drawing and scale coincide (in ap- 
pearance). The paper should be held at the distance of 
distinct vision. 

If now each tenth of a millimeter on the drawing mea- 
sures 3 millimeters, the power is 30, etc. 

287. Observe 1 various minute objects (compare 253), and 
also enter proper record of your observations in your 
Journal, illustrated by carefully drawn sketches. 

If you make the sketch of precisely the magnitude which 
the object appears to have in the microscope, the sketch 
will be a drawing to the scale of the magnifying power. 
Thus if the microscope magnifies 30 times, the sketch will 
be a drawing to the scale B0 / t and should be so marked. 
Compare 66. Also, 193. 

288. Microscopes are often provided with a polarizing 
apparatus, which is exceedingly useful and interesting. 

The polarizing apparatus consists of two parts, the polar- 
izer and the analyzer. The polarizer is placed on the stage 
of the microscope immediately below the object. The an- 
alyzer may be put on top of the eye piece. 

289. By rotating the analyzer, the field of view will 
alternately be bright and dark. If bright, the analyzer 
must be turned a right angle to darken the field — after an 
additional rotation of 90 degrees the field will be bright 
again, etc. But if the field is dark, we need only to re- 
move either the analyzer ar the polarizer in order to have 
the field bright again. 

Thus it appears that two .transparent bodies may, ac- 
cording to their relative position, either transmit or absorb 
the light. 

*It is best to have a micrometer, or a millimeter divided into 50 or more equal 
parts. 

16 



122 Chapter IV. 



290. If a dr >p of common salt, another of nitre, a 
third pf copper vitriol is brought on a glass slip and the 
crystals observed through the darkened polarizing appa- 
ratus, the crystals of salt will leave the field dark, while 
the others will brighten it and can show beautiful colors, 
provided the crystals are exceedingly small. In general 
all crystals, except the tesseral ones, (see 199) will thus 
brighten and color the dark field of the polarizing micro- 
scope. 

In this manner we can determine whether a crystal is 
tesseral or not, even if it be exceedingly minute. 

Most organic materials, such as hair, starch, etc., also 
brighten the dark field in the polarizing microscope. 

All such bodies are said to be double refracting. 
VI. APPENDIX. 

291. Double refraction is most easily observed in na- 
tive crystals of caleite or Iceland Spar (compare 165 and 
199) and the artificial crystals of sodium nitrate, (see 186 
and 198.) 

You need only put a smnll clear cleavage piece of the 
former or a transparent crystal of the latter (about 5 mm. 
long is quite sufficient) on a piece of white paper on which* 
you have made a very fine point or line. These will ap- 
pear double through the crystal. If need be, use the mag- 
nifying glass. 

Carefully observe the two images while the crystal is 
rotated on the paper. Record the result of your observa- 
tion in your journal. Are both images equally movable 
or equally fixed ? Make, if possible, correct drawings in 
reference to the position of the crystal ! 

292. Look through a rhombohedron of the same sub- 
stances, but in the direction of the axis which joins the 
two obtuse corners of the crystal. This can be best ac- 
complished, if these corners have been ground off plane 

and at right angles to that axis. 

© © 

Does the point appear double in this direction ? 



Photometer. 123 



293. The direction in which a crystal does not possess 
double refraction is called the optical axis of the crystal. 

Triclinic, monoclinic and rhombic crystals have two op- 
tical axes. Hexagonal and quadratic crystals have one 
optical axis. Tesseral crystals have none, or rather they 
possess no doable refraction at all. Compare 199. 

How many optical axes has nitre ? common salt ? cal- 
cite? etc., etc. 

294. If from a crystal with one optical axis a plate is 
cut at right angles to that axis, and placed in the dark field 
of a polarizing microscope of very low power, a dark cross 
only will remain, while the balance of the field shows a 
system of beautifully colored rings around the center of 
that cross. These curves are often called the isochromatic 
curves of monaxial crystals. 

295. If the plate had been cut from a crystal of two 
optical axes, so that the plate is equally inclined to both 
axes, a cross will appear under the same circumstances, but 
surrounded by a very beautiful system of colored curves 
termed the lemniscates. Observe a plate of nitre, about 
2 mm. thick. These curves are often spoken of as the iso- 
chromatic curves of binaxial crystals. 

296- The simplest polarizing microscope is the turma- 
line tongue. It may be used for these last observations. 
(294 and 295). 

297, The simplest photometer consists of a small round 
rod of about the thickness of a common pencil and twice 
as long, placed vertical in front of a white square screen 
about 30 cm. squara; the rod being distant about 10 cm. 
from the screen. 

Place this photometer on a table in a dark room (on a 
dark evening), and put the two sources of light to be com- 
pared in front of the same. Move one of the sources of 
light until the two shadows on the screen are just in con- 
tact and also equally dark. Then the illumination of the 
screen is equal by the two sources of light. 



124 



Chapter IV. 



298- As standard source of light — 1, take a burning 
stearine candle. Place it at any distance directly in front 
of the above photometer; measure the distance =D. 
Then place successively 1, 2, 3, 4, 5, etc., burning can- 
dles of the same quality, all mounted on the same wooden 
block in one row*. Measure the distance d from the 
screen to the middle of the row of n burning candles. 



Record the result thus 
Series I. 



No. 



n 



D= . 


. . . , hence 1 

D 2 ~ 


d 


« d2 

1 d 


n 

d 2 



It will soon be seen, that the number of burning candles 
divided by the square of the distance is uearly equal for 
all cases, and also to that for the normal candle. The dif- 
ferences e between n_ and 1_ are indeed small, if the ob- 

d 2 D 2 
servations were made with care. 

299. Hence the law of action of light in distance is 

n 

-r 2 = constant. 

or the intensity of illumination on a given plane is in- 
versely proportional to the square of the distance. 

300. This law is quite universal. It applies to all phy- 
sical agencies not only to light, but also to heat, sound, 
magnetism, electricity (see next chapter) and also to the so- 
called force of gravitation. 



♦Have those nearest the photometer burn down more than the others, so that each 
flame can illumine the shade unobstructed by its neighbors. Also keep the candle 
in line with the rod of the photometer! 



CHAPTER V. 



ELECTRICITY AND MAGNETISM. 



/. On Magnets. 

301* The common horse-shoe magnet (fig. 43.) is the 
most convenient source of magnetic power for the stu- 
dent's use. A few bar magnets, one dm. long and one cm. 
square should also be obtained. 

302- When not actually in use, the keeper (a b fig. 43) 
of soft iron is brought in contact with the magnet, as shown 
in the figure. This is done in order that the magnet may 
keep its strength. 

303. Substances which are attracted by the magnet, 
are said to be magnetic; all others are said to be non-mag- 
netic. 

Have small pieces (about one mm. thick and a few mill- 
imeters long) of different substances, in a paper box, and 
dip the magnet* into the box, and observe which bodies 
are magnetic. Record the results in your journal. In 
this manner try at least brass, zinc, copper, iron, steel,f 
glass, wood, paper, fragments ot limestone. In a separ- 
ate glass tube may be kept a little aluminium sheet or 
wire, cobalt, and nickel.^: These metals are also care- 
fully tested. 

304- A body is magnetized if it acts like a magnet, 
not only being attracted like a magnet, but also itself at- 
tracting other magnetic substances. 

If a magnetized body retains its magnetic power, it is 
called a permanent magnet. If it loses the power upon 

♦From which, of course, the keeper has been gently removed. 

fRecognized by its hardness ; if not hardened, steel acts like iron on the 
magnet. 

tXickel has green spots from corrosion. Aluminium is white in wire. 



126 Chapter V. 



the withdrawal of the cause which magnetized it, the mag- 
netized body is simply a temporory magnet. 

305. Study the properties of perfectly soft iron and 
well hardened steel in this regard.* Bring the body — 
about five cm. long and one mm. thick — w r ith one end in 
contact with one extremity of the horse-shoe magnet (301) ; 
and to the other end of the iron or steel present some fine 
iron filing, some very small nails, etc. Carefully observe 
the effect. Then remove the horse-shoe magnet from the 
iron or steel, and observe whether the magnetized condi- 
tion remains or not. Record the results of your observa- 
tions in your journal, with special reference to the terms 
defined in 304. 

306. To magnetize the sewing needle — or any other 
piece of hardened steel — more strongly, draw one ex- 
tremity of the horse-shoe magnet several times forcibly 
along the entire length of the needle, always in the same 
direction. This operation is called magnetization by the 
single touch. 

307- For reasons which will become plain in the 
subsequent, take that end of the horse-shoe which is 
marked S, or in the absence of this letter is not marked 
N ; and move this part of the magnet from the eye toward 
the point of the needle. 

Also magnetize a blade of your pen-knife in the same 
manner, from the handle towards the point; you thus ob- 
tain a very useful pocket-magnet. 

308- Dip either of the small permanent magnets thus 
prepared into fine iron filing. Upon taking up the magnet, 
the filing will be found adherent mainly at the extremities 
of the magnet, while none adheres in the middle. 

309. Accordingly the attractive power of magnets is 
greatest near the extremities and smallest near the middle. 
The former are called the poles of the magnet, the latter 
the equator (or neutral zone). 

The power peculiar to magnets is called magnetism. 

♦Soft iron wire — if need be, soften it yourself by heating it to redness and slowly 
cooling the same ; as steel, use a fine sewing needle. 



Oil Magnets. 127 



310. To more fully examine the distribution of the 
magnetic force in a magnet, cover the magnet with apiece 
of card paper,* and sieve some line iron filings upon the 
card. The beautiful magnetic curves^ also called the mag- 
netic phantom, will then form, especially if the edge of 
the card be gently tapped with a finger. Draw an accur- 
ate sketch of these lines in your journal. 

311. The extremities of magnets are not only centres 
of greatest magnetic force, but they exert also a directive 
influence in reference to the surface of the earth. 

To make this fact apparent, the magnet must be sup- 
ported so that it can freely move at least in a horizontal 
plane. 

312- By placing a small magnet — for example, the 
magnetized needle — on a disk of cork which floats on 
water, contained in a saucer, the magnet can turn freely 
in a horizontal plane. It will soon come to rest in a posi- 
tion nearly north and south. 

313. The same end is better attained by putting the 
magnetized needle twice through a small piece of this 
paper, which again is suspended by a long hair or a fine 
fibre of silk to some convenient support. Also in this 
way the needle will soon assume a fixed direction, nearly 
north and south If removed from it, the needle vill, 
after some oscillations, return to the same. Accurately 
observe all this. 

314. That extremity of the magnet which now points 
towards north is called the north end or north pole. The 
other extremity pointing south is called the south end or 
south pole of the needle. 

315. In order to ascertain the name of the poles of 
any small magnet, it is therefore only necessary either to 
float the magnet on water or to suspend the same bv alono; 



*The extremities of the common horse-shoe magnet can for this purpose be 
slipped into two corks, properly cat our and fastened with sealing-wax to the card. 
The card is held horizontal by holding the magnet vertical. 

But even a magnetized sewing-needit will show some curves. 



128 Chapter V. 



and sufficiently fine thread. In this way it will be found 
that the pole stamped N, or north, on the horse shoe 
magnets is the north pole. 

316. The magnetization by single touch (306) perform- 
ed as directed in (307) will in this manner be found to have 
made the point of the needle a north pole, the eye a south 
pole ; the magnetizing pole used was a south pole (S). 

317- It may be concluded from this, that the poles of 
the new magnet formed by single touch are such as to cor- 
respond to a simple addition in length of the magnetizing 
magnet. The free end (the eye) formed the same pole 
(south) as the magnet pole used. 

By repeating this experiment under other circumstances, 
the rule is found to be correct in all cases. 

318- The action of magnetic poles on one another 
must be determined qualitatively (in kind) and quantita- 
tively (in amout or intensity). The former is quite easy ; 
the latter cannot be treated of in the elements of physics 
— but is found to be the same as 299. 

319. To determine the qualitative action of the mag- 
netic poles on one another, take two magnetic needles, i e., 
magnetized sewing needles. Determine their poles by 
suspension (315). Thus leave one suspended and present 
alternately the poles of the other to each of the poles of 
the former, and record the effect in your journal. Express 
the action ; n a general law by using the terms like poles 
for poles of the same name and unlike poles for poles ot 
different names. Write it down plainly. 

320- This law of the qualitative action of magnetic 
poles on one another, is a most important natural law; it 
reappears again in many other branches of physics and 
chemistry, and even in some very peculiar phenomena of 
vegetable and animal life. 

321. By means of this law it is easy to ascertain 
whether a given body is magnetized or merely magnetic ; 
and if magnetized, the precise location of the poles is 
equally readily determined. 

If both the poles of the magnetic needle (313) are at- 
tracted by the body, the latter is, of course, merely mag- 



On Magnets. 129 



netic ; if one of the poles is repelled, the body is magnet- 
ized, and the repelled pole resides at the point investi- 
gated. 

322- With such a small magnetic needle test the con- 
dition of some iron and steel tools, a stove, stove-pipe, iron 
pillars, bars, etc., which may be at hand. Record the re- 
sults in your journal. 

Also test in the same manner different minerals, especial- 
ly iron ores. 

323. The black iron ore, is always magnetic (303); 
hence it is commonly called Magnetite (( ompare 165, No. 4). 

But many pieces of this ore are also perm u ently mag- 
netized, thus constituting real natural mag tuts. These 
are known as lodestones (vulgarly loadstones), 

324. Experiment with such a natural magnet ; enter a 
sketch of its form in your journal, determine the posi- 
tion of its poles (321) and mark them on your sketch. 

325- The steel-magnets are now distinguished as arti- 
ficial magnets from the lodestones. Formerly steel mag- 
nets were all originally made by touch with natural mag- 
nets (see 306). Now we have also other very efficient 
modes of magnetizing steel ; see electro-magnetism. Quite 
large and powerful magnets in the shape of bars are now 
made ; we call these magnets bar magnets. 302. 

326. The two poles of a magnet cannot be separated. 
If a magnetized sewing needle is broken in two, both 
pieces will still each possess a north and a south pole. Prove 
this by testing bot'i fragments, according to 321. De- 
scribe the test in your journal. 

327. The magnetic needle is extremely useful especial- 
ly in navigation, surveying, and physical science. Its 
most common application is the compass. Any magnetic 
needle which is supported so that it can freely turn in a 
horizontal plane, can be used as a compass. Often the 
needle rests on a steel point by an agate cap fixed in its 
middle. This you will see in any good compass. 

328. A very sensitive compass may readily be made 
by attaching a magetized sewing needle by means of seal- 
ing wax, to a single silk fibre, which again in the same 
manner is fastened to a pin, passing through a cork insert- 
ed in the top of an inverted glass funnel. The funnel is 
placed on a piece of wood on which a graduathd circle has 

17 



ISO Chapter V. 



been pasted. The simplest way of stopping its vibrations 
is by bringing the needle in contact with the divided circle; 
or by means of a magnet (see 329). 

329. At a distance of more than a meter south or 
north of such a compass (328) hold a bar-magnet, and 
turn the poles of this latter alternately towards the needle ; 
be careful to always present that pole at the very time 
w T hen it will accelerate the oscillation of the needle if left 
alone. You will then see that the first very slight deflec- 
tion to each side becomes greater and greater, until you 
finally may throw the needle entirely around in its plane. 

This requires rather delicate manipulation, and accurate 
appreciation of time. 

By reversing the order, you can gradually and most ef- 
fectually stop the vibrations of the needle. 

330- Such a compass shows also how magnetism acts 
through all non-magnetic bodies, such as wood, glass, paper, 
etc. For the experiment, 329 may be repeated with the 
same success, even if either of the above substances have 
been placed between the bar-magnet and the needle. 

II. THE EARTH-MAGNET. 

331. The fact that most iron and steel which has for a 
length of time remained in a nearly vertical position, has 
become magnetized, proves that the earth is itself a huge 
magnet. Compare 305. The great iron ships are always 
more or less magnetized from the same cause. 

332. We shall first study terrestial magnetism, that is, 
the magnetic properties of the earth, by. means of the 
compass. 

333. If a compass like 328 is adjusted, so that the 
diameter marked zero is directed due north and south, the 
magnetic needle will in most places form an angle of several 
degrees with this line. 

334. The angle between the true north south direction 
and the magnetic needle, is called the magnetic declination 
or variation. 

It is very different in different parts of the earth's sur- 
face. Here we can only describe how the magnetic de- 1 
clination varies in the United States. 



The Earth-Magnet 131 



The student should, as carefully as possible, determine 
the declination at the school building, making use of the 
north and south line (meridian) which the teacher has de- 
termined beforehand. 

335. On a line running from near Cape Lookout (N. 
C.) towards the middle of Lake Erie, the magnetic needle 
points true north and south. On this line the declination 
is therefore zero. The above line is also called the line of 
no variation. 

336- In that portion of the United States west of this 
line, the magnetic needle points East of true north ; hence 
the magnetic declination is said to be East in the part of 
the United States above mentioned. 

337. To the east of the above line of no variation, the 
magnetic needlepoints west of true north, or the magnetic 
declination is west. 

338- The declination is continually and slowly chang- 
ing in time. In our western states the declination is slow- 
ly decreasing, while in the east it is increasing. The 
amount of this change is about five minutes a year for 
most parts of this country, (U. S.) or one degree in about 
twelve years. These changes are called secular. 

339. By more refined instruments it has been found 
that the magnetic needle is constantty in motion, describ- 
ing a more or less regular oscillation each day. These 
changes are termed daily changes. 

340. At certain times these smaller changes in the 
position of the magnetic needle become quite perceptible, 
and also more sudden. This is especially the case imme- 
diately before and during the display of Northern Lights. 

This disturbance of the needle is quite manifest also in 
those regions of the earth where the Northern Light (Au- 
rora Borealis) is not visible. Thus the magnetic needle 
can inform the southern resident that the polar sky in the 
far north is adorned by a brilliant display of light and 
color. 



132 



hapter 



III. FRICTION ELECTRICITY. 

341. A glass rod, about twenty cm. long and five mm. 
thick, is slowly drawn through the gently closed hand* 
and then held near some tine paperf cuttings, which for 
this purpose may be kept in a shallow paper box. The 
effect is noted and recorded in the journal. 

342. Now vigorously rub one-half of the length of the 
same glass rod with a piece of silk. Present the rubbed 
glass and thereafter also the rubbed silk to the paper clip- 
pings ; carefully observe what happens ! Then gently 
draw the glass rod again through the hand, and try again. 
Do the same with the silk. Record all your observations 
accurately and concisely in your journal. 

343. Experiment in precisely the same manner with 
at least a few of the following solids : Sealing-wax, wood, 
metal-rod, (iron, brass ; or the like), hard-rubber, (a piece 
of comb will answer) ; also, a bead of amber, a piece of 
resin. 

Instead of the silk or rubber use a piece of flannel, or 
a piece of fur (especially the fur of a cat or fox) and the 
like. 

Record all results carefully observed, also in regard to 
the intensity of the effect noticed ! 

344. Bodies, which after such friction attract all sorts 
of light bodies are said to be electrified by friction, and 
the peculiar force now resident in them is called friction- 
electricity. When thus electrified, bodies are also said to 
be excited, while when this peculiar force has disappeared 
they are again said to be in their natural condition. 

345. Which of the preceding bodies are electrified by 
friction ? Which the most? Which the least? Is glass 
more excited when rubbed with flannel, or with silk, or 



*In all experimentation the hands should be kept clean, as a matter of course. 
But in electrical experiments unclean or moist hands will always completely pre- 
vent the electrical result from becoming observable. 

■jTissue paper 4 is best; the cuttings should be one by ten mm. 



Friction Electricity. 133 



with fur ? How is sealing-wax in this regard ? Answer 
all these and similar questions in your journal by refer- 
ence to your experiments 343. 

346. The electroscope shows whether a body is electri- 
fied or not. The simplest possible electroscope is there- 
fore the box with fine cuttings of tissue paper (341). The 
following electroscopes are for most purposes better, and 
some of the experiments of 333 should be repeated with 
these electroscopes : — 

347- The electrical pendulum, consisting of a small 
pith ball suspended by means of a silk string to some non- 
metallic support. 

348- The electrical needle consists of a fine glass rod 
(or a fine glass tube closed at both ends) suspended by a 
silk threat!, like a magnetic needle (313) and provided with 
a small pith ball on each extremity. Instead of the pith 
ball you can use fiat disks of sealing-wax coated with a 
piece of tin foil on each side. 

349. The two electricities. The electricity developed 
on glass by rubbing it with silk is called glass electricity or 
vitreous electricity. The electricity developed on sealing- 
wax by rubbing it with flannel is called resinous electricity. 

350. We can, of cousse, adopt these definitions ; but 
in order that they may possess any real value, experi- 
ments should prove that these two electricities are differ- 
ent from one another. The following is the most elegant 
and simple method of performing such experiments : — 

351. Take two glass rods, each about twenty cm. long 
and five mm. thick. Each of these rods is for half its 
length, thinly but completely coated with red sealing-wax.* 
One of these rods suspend in a paper stirrup by a silk 
string (about twenty cm. long) so as to constitute an elec- 
trical needle. 

Rub the red sealing-wax extremities with the red flan- 
nel ; then they will possess resinous electricity. Also, rub 
the clean glass extremities with silk; then these latter 
will possess vitreous electricity. 

*By rubbing the heated rod against a stick of sealing-wax. 



134 Chapter V. 



352- Now present the two extremities of the second 
rod successively to the two extremities of the suspended 
rod or electrical needle. Always carefully avoid any real 
contact between the two rods. Also, hold the rods only 
in the middle, between the thumb and the first finger; 
have your hand carefully dried and cleaned from all per- 
spiration. 

Record each result observed in your journal ; try to ex- 
press all results in one law, by using the terms like and 
unlike electricities. Compare 319, 320. 

353. By means of this law (352) it is easy to determine 
which kind of electricity a body possesses by presenting 
the same to either extremity of the above electrified elec- 
trical needle (352), or to either of the electroscopes, 347 
and 348, after having charged these with a known kind of 
electricity. 

354- Practice the use of the same by repeating some 
of the experiments of 343. Record the results in your 
journal. It will then be found that all those bodies possess 
either vitreous or resinous electricity. Hence there are 
only two kinds of electricity. 

355. Vitreous electricity is often denoted by +E, and 
named positive electricity. Resinous electricity is then 
denoted by — E, and named negative electricity. These 
names were first proposed by Benjamin Franklin. 

356- Very thoroughly and carefully electrify the two 
ends of the electrical needle, 351 ; then you will find that 
the silk has thereby become electro-negative and the flan- 
nel electro-positive (353). But this you can only prove if 
you are extremely careful in every respect. It is easier 
proven for flannel than for silk. 

357- Accordingly* by friction both electricities are pro- 
duced at the same time / thus : 

1. Glass (+E) and silk (— E). 

2. Sealing-wax (— E) and flannel (+E). 

358. The natural or neutral electrical condition of a 
body may therefore be compared to a lever in equilibrium 

*We state the true result here because the experiments are difficult indeed. 



Friction Electricity. 135 



and horizontal. By friction this condition is disturbed, 
in opposite directions, for the bodies rubbed against one 
another assume opposite electricties ; precisely as one of 
the arms of the lever moves down while the other moves 
up. 

359- Hence it is also customary to say that the neutral 
electricity of a bod} r is decomposed by friction into +E and 
— E. 

360. Suspend awire* of any metal — say asteel-knit- 
ting wire — in the same manner as the electrical needle 
(318). Draw the same gently through the fingers, so that 
it is in neutral condition. Then it will, as well as any 
other light neutral body, be attracted by the rubbed glass 
and also by the rubbed wax rod. 

361- If you now permit the attracted wire to touchf the 
excited glass rod, it will, after some little time, be strongly 
repelled from the same. It will continue to repel the 
glass-electricity, but be attracted by the wax-electricity. 

362. The wire therefore has become charged with the 
electricity of the glass rod, by simple contact with the 
same. 

363. But not only the extremity which was touched — 
also the other extremity of the wire is now repelled by 
the glass rod and attracted by the wax. 

364- Hence the positive electricity communicated to 
one end of the metallic wire by touching the glass rod, 
has been transmitted along the metallic wire to the other 
extremity of the same. 

365. If the experiment is repeated with — E (wax ex- 
tremity), a like result will be obtained. 

366. Accordingly both electricities are easily trans- 
mitted along the metallic wire. Metals are therefore called 
good conductors of electricity. Indeed, it is found that the 
length of the wire is of hardly any consequence. 

*The wire must have well rounded ends. 

fit is best to gently move the rod up and down, sliding against the a wire, so that 
the latter conies in contact with many points of the rod. 

I 



136 Chapter V. 



The human body is also a pretty good conductor. Hence 
by drawing the glass rod through the hands, its electricity 
is removed. 341. 

367. If we take a glass rod, instead of the metallic 
wire, we find that no electricity will be transmitted from 
one end of the rod to the other. That is, glass is a poor 
conductor or even a non-conductor. Sealing-wax, sulphur, 
hard rubber, silk, etc., are also non-conductors. The air is 
also a non-conductor. 

368. If a metallic body be surrounded or supported in 
dry air by such a non-conductor, no electricity can pass off 
from the metal. The latter is then said to be insulated, 
and the non-conductor used is called the insulator. 

369. If the wire has one of its extremities ending in 
a sharp pointy it will not become charged, but remain in 
the neutral state — for it will not be repelled. Since now 
by contact electricity does pass to the wire, (see 362) it 
must continually pass <^f atthe point. 

370. That this is really so may best be seen by repeat- 
ing this experiment in the dark. The pointed extremity 
of the wire will then exhibit a luminous brush, while the 
wire is in contact with the electrified rod. 

371- This action of points was first investigated by 
Benjamin Franklin. His lightning-rod is an excellent ap- 
plication of this principle. 

372. When a piece of a hard rubber comb is vigorous- 
ly rubbed by a piece of fur, (cat) you will hear a crackling 
noise and if the experiment is performed in the dark, you 
will also see small sparJcs of light. These electrical sparks 
are also produced by presenting a knuckle to the excited 
rubber comb. Less readily the same phenomena are ob- 
served when sealing-wax has been rubbed with flannel. 

373. By means of the electrical machine, more intense 
electricity may be collected, giving not only more vivid 
sparks, accompanied by louder reports, but also capable of 
strongly shocking man and animals. This proves that 
lightning is an electrical spark. 






Friction Electricity. 137 



374- The common electrical machine consists essen- 
tially of four parts : the rubber and the glass plate for the 
exciting of electricity and the comb of points for collecting 
the positive electricity from the glass. The comb is attach- 
ed to the prime conductor, a metallic cylinder acting as a 
reservoir for this electricity. 

375. JFor a description of such machines, we must 
refer to a subsequent volume. The same remark applies 
to the Leyden jar and the electrical battery used for con- 
centrating the electricity to a greater degree than possible 
by the prime conductor of the machine. 

376. If an electrical machine and a few Leyden jars be 
at hand, we advise the teacher to exhibit both and also per- 
form and explain a few of the most important and inter- 
esting experiments with this apparatus before the stu- 
dents. The students should enter an abstract of these ex- 
planations in their journal. If they have carefully studied 
and practiced the preceding articles, they will have not the 
least difficulty to understand all the experiments thus ex- 
hibited. The teacher should, of course, only perform ex- 
periments which are strictly elementary. 

377. Friction was the source of electricity made use 
of in the preceding ; it is, also, the source of electricity in 
the common electrical machine, 376. But by friction me- 
chanical work is consumed (101 and 102). Hence it ap- 
pears that eiectricity is obtained as a return for the me- 
chanical work consumed by rubbing glass, sealing-wax, 
and like materials. 

378. It has also been sufficiently demonstrated, that 
the electrical power thus produced is indeed equivalent 
to the mechanical power (work) consumed. 

379. The so-called electro-machine, invented by Holtz, 
of Berlin, in 1866, forms the very best demonstration of 
this fact. A minute quantity of electricity, produced by 
rubbing a piece of hard rubber with a cat's fur, is applied 
to the machine, while one of the glass plates rotates. 
Immediately the force required to rotate the plate in- 
creases, and at the same time the electrical force increases, 
until it becomes strong enough to force its way through a 

18 



138 - Chapter V. 



great distance in the air (spark). In this machine, almost 
all the mechanical work applied to the machine is returned 
in the shape of electricity. 

380- The effects of electricity can be exhibited to 
much greater advantage by means of this machine than 
by any other yet invented. If but a short distance of air 
intervenes between the two electricities constantly pro- 
duced by the rotating plate, they unite in the shape of a 
luminous brush/ if a larger distance of air (367) inter- 
venes, the two electricities unite at regular intervals of 
time, forming a brilliant spark, producing a loud sound — 
we have then lightning and thunder on a small scale. If 
a good conductor (366), such as a copper wire, connects 
the two electricities, they unite, forming an electrical cur- 
rent, the presence of which can best be shown by the mag- 
net (see 401 to 405). 

IV. GALVANISM. 

381. The simplest galvanic cup or galvanic element 
consists of a piece of zinc sheet Z and a piece of copper 
sheet, C, both partially immersed into very dilute sul- 
phuric acid,* A, figure 44. The metallic plates should be 
parallel to one another, at a distance of about five mm., 
and they should be insulated from one another (368). 

382. By sufficiently delicate electroscopes, it has been 
shown that the zinc plate projecting above the liquid, 
is feebly charged with negative electricity. In the same 
manner it has been ascertained that the projecting part of 
the copper plate contains positive electricity. Our electrical 
needle (348) is not sufficiently delicate for this purpose. 

383. The projecting parts of the two plates are called 
the poles of the galvanic element. Accordingly the free 

*The pieces of sheet metal need not be larger than two by five cm. They may be 
held by means of the cork to which they are fastened by sealing-wax. The dilute 
acid is obtained by slowly pouring one cc. common sulphuric acid into twenty-five 
cc. of water, while stirring the latter. 



Galvanism. 139 



zinc-extremity is the negative pole, while the free copper 
end is the positive pole of this galvanic cup. 

384. If the element be closed, its two poles being con- 
nected by means of any conductor — say a copper wire — 
the positive electricity must (364) flow from the positive 
pole (copper) through the conductor to the negative pole 
(zinc) and from this through the liquid to the copper. The 
negative electricity flows in the opposite direction. 

385. Accordingly we may consider the closed galvanic 
element as pervaded by two currents of electricity : a cur- 
rent of positive electricity passing from the zinc through 
the liquid to the copper, and through the conductor back 
again to the zinc. Also a current of negative electricity 
circulating in the opposite direction. 

386- For the sake of brevity, only the current of pos- 
itive electricity is commonly referred to when a galvanic 
current is spoken of. Hence the galvanic current in the 
above simple cup flows from the zinc through the liquid to 
the copper, and through the conductor back to the zinc. 

387- The preceding facts cannot readily be directly 
verified by the student ; we therefore are compelled to 
merely state them here for use. But indirectly they will be 
fully demonstrated in the subsequent sections. 

388- But even here we can by a very simple experi- 
ment demonstrate the presence of the peculiar activity 
denoted above as a galvanic current (386). We need only 
dip two small platinum strips connected each with one of 
the poles into the solution of blue vitriol. The strip con- 
nected with the negative pole (383) will almost immediate- 
ly* be colored red from the deposition of metallic copper 
separated by the current from the solution ! The strip in 
connection with the positive pole of the galvanic element 
will remain clean. 

389- Now exchange the two strips, connecting the red- 
dened strip with the positive pole, etc. Observe, and 
record ! 



♦Provided the strips are only one or two mm. distant from one another in the so- 
lution. 



140 Chapter V. 



390- It thus appears that indeed some peculiar activ- 
ity is transmitted through the conductor, an activity indi- 
cated by the separation of metallic copper from the solu- 
tion of blue vitriol. This particular action of the galvanic 
current is termed a chemical action, often also denoted as 
electrolysis. The galvanic current produces, however, 
many other effects, some of which will be studied in the 
subsequent. 

391- The deposition of copper on the metallic con- 
ductor connected with the negative pole of a galvanic ele- 
ment is extensively used in the arts for the manufacture 
of electrotypes and in galvanoplastics. 

392. From solutions of gold and silver, these metals 
are also separated by electrolysis, for the purpose of gild- 
ing and silvering, the manufacture of plated ware, etc. 

393. To produce a nearly constant and quite abundant 
galvanic current for such purposes, various galvanic ele- 
ments have been devised. It has been found that the 
power of the current is modified in three ways, by the 
size of the plates, by the kind of plates and liquid used, 
and by the number of elements combined. 

394- The greater the size of the plates, the more abun- 
dant the amount of electrical activity. The greater the 
number of elements combined in one and the same direc- 
tion — the zinc of the one always connected with the 
copper of the next — the greater is the intensity of that 
activity. Any number of elements thus combined consti- 
tutes a galvanic battery. 

395. The galvanic current resembles in these two 
respects a current of water. The size of the plates cor- 
respond to the size of the canal in which the water flows, 
while the number of elements correspond to the height 
through which the water falls. 

396. The zinc-copper-sulphuric acid element above de- 
scribed is quite useful. Many cups may be combined to 
form a battery. 

But the elements comparatively soon lose their power. 
If the zinc has been amalgamated* the cup works longer ; 

♦This is done by rubbing a drop of mercury on the ziucjafter it has been cleaned 
and corroded by immersion in the acid. 






141 



*n the zinc will not be much attacked by the acid 
except while the circuit is clo B4). However, even 

in this case, the metals should be lifted out of the liquid 
when the current is nut actually required. 

397- A simile zinc-copper batttrry. which will work for 
a long time without refilling, has been described y Secchi, 
in the London Laboratory^ for June 22, 1867. We quote 
his very useful description below,* complete, so that the 

♦This battery, which is to work the meteorograph exhibited by me in the Korean 
Court of the Paris Universal Exhibition, is constructed on Danieil's principle, the 
porous diaphragm being replaced by sand, in the following manner: A piece of 
thin copper plate, about fifteen centimeteres square, is cut into six points at one 
end. The points are alternately bent into a horizontal position, and the pla:v is 
then rolled into the form of a hollow cylinder, the edges being - ■: '. lered together, 
ehed to connect it with the next element. The thw verti V. | bits 
thus act as a tripod to support the cylinder, and may be about four or five centi- 
metres in height. The copper cylinder is introduced into a glass vessel of about 
en centimetres in height, and ten in diameter, containing four or five centi- 
metres of sulphate of copper. The vertical points of the copper cylinder are forced 
through the crushed sulphate, so that the horizontal poh r. 

Two discs of thick, bibulous paper, of the same diameter and 

per: a to fit tightly round the copper cylinder, are placed on the sur: : 3 

of the sulphate of copper, and carefully pressed down so as to leave as little air 
as possible below them, and to prevent any mixture of the sulphate with the sand. 
On to ind of about one centimetre in depth, is placed, and upon 

this a common zinc cylinder of about ten e n i m etres in height an 1 seven in 
meter. When the zinc is in its place all the space between the zinc and the copper 
and the zinc and the glass is filled with sand to within about two centimetres from 
the edge of the glass vessel. 

The battery is cow ready for use, and is charged by pouring water into the exte. 
rior en the m nd until it reaches to about a centimetre from the edge of the vessel. 
The water should never be pcureel into the copper cylinder, but always on the outside. 
A- the :lphateof copper is decomposed, fresh quantities are added through the 
copper cylinder, and it is well to fill the cylinder with powdered sulphate before 
placing the water in the outside, as this produces greater density in the solution and 
stronger action. 

Th sand should be free from all calcareous matter, therefore pure siliciou= a 
should be selected, or common sand should be washed with dilute nitric acid, andall 
traces of acids and salts aftei wards removed with the greatest care by long washing. 
:ju of activity of this I ittery is the mc sf -imple possible. There being 
no addition of free acid, it is the equivalent of acid which leaves the copper in the 
sulphate to combine with another equivalent cfzin:. bc thai action can go on in- 
definitely, and with constant force, as Ion g - there remains salphate of copper to 
be decomposed. In practice this battery lasts until the sand is saturated with sul- 
phate of zinc, and this crystallizes in the cells round the zinc and amongst the sand. 
that it may last for a whole year without changing the sand or 
removing the sulphate of zinc when the battery is in action for twelve hours a 
it is in the meteorograph. For common clocks and ringing bells it lasts 
commonly in Eome for eighteen months or two y 

Its torce is about one-half of Danieil's battery, and between one-fourth and one- 
fifth of Bunsen's battery, so that five cells united for quantity can replace one of 
Bunsen"s cells. 

When the battery is dismounted, after its action i3 exhausted, the zinc is general- 



142 



Chapter V. 



teacher can have such battery constructed for use in the 
school-room. 

398. Meidinger's battery remains active for several 
months when in in constant activity. It is used by the 
German telegraph companies. We give below* suf- 
ficient directions to construct Krueger's improved and sim- 
plified form of this battery. 

399- The most powerful — but also most expensive, 
and by far the most troublesome — galvanic batteries, are 
those invented by Bunsen and Grove, and known as the 
Bunsen battery (amalgamated zinc — dilute sulphuric acid 
— porous cup — concentrated nitric acid — solid carbon) 
and the Grove battery. In the latter the carbon is re- 
placed by platinum. 

400. In all experiments with the galvanic element or 
batteries, it is absolutely necessary that the connections 
should he pure and metallic. Hence a file should be at 
hand, to clean the wires and other metallic pieces, which 
are to be connected. The connecting wires should consist 
of copper, and wound so as to form a screw-line. The 
wire ought to be covered with cotton or silk, and sufficient- 
ly thin to be easily bent. 



ly found thickly coated with a layer of sulphate; this is easily removed by washing 
with water, and after a second washing with dilute sulphuric acid the zincs are again 
ready for use, and will last for another year or two. Several of my zincs have been 
in use for three years. The zinc should be of good quality ; common commercial zinc 
if pure and cast, will answer very well without any amalgamation. A cast zinc is 
known to be of good quality by its sound, which is very sharp and acute, and rings 
like a bell. If the souud is dull, then there is lead in it, and the action will be very 
weak. 

♦Lead water tube eight cm. long, two to three cm. wide, stands by three or more 
outward-curved feet, formed by splitting the lower end of the tube, on the bottom of 
a 'jlass vessel, partly filled with a solution of magnesium sulphate (epsom salt) in 
eight times its weight of water. By copper wires resting upon the rim of the glass, 
a zinc ring (four em. diameter, three cm. high), is suspended around the upper half 
of the lead tube. Stout copper wires have been soldered to both the lead pipe and 
to the zinc rinu r , serving for the attachment of the conductors. 

Some lumps of blue vitriol are from lime to time thrown into the lead tube, to keep 
the cup active ; it needs no other attention for two to three months, if it is kept con- 
stantly closed. 



Eledro-Magn etism . 1-43 

V. ELECTRO-MAGNETISM. 

401. Bring the conductor (wire) through which a gal- 
vanic current passes, near a magnetic needle (313). The 
needle ic ill ie deflected by the galvanic current. This is 
(Ersted's discovery. 1520. 

402- Magnets are thus acted upon by galvanic cur- 
rents, and of course the latter are equally acted upon by 
the former. 

403- All interaction of magnets and galvanic cur- 
rents constitutes electro-magnetism. 

404. Suppose yourself floating in the galvanic cur- 
rent, head foremost and facing the needle; to what side 
(right or left) will the north end of the needle be deflected, 
when you hold the current above or below the needle, and 
in each position have the current flow from south to north 
or from north to south. Record your observations in your 
journal, thus : — 

Position of Current. | Direction of Current, j Deflection of Xeeclle. 

405. Can you express these results in a general law? 
Ampere's law. 

406- What will accordingly be the action of a gal- 
vanic current flowing jn a circle around the magnetic 
needle? First, by means of Ampere's law. And out the 
direction in which the north end will be deflected if the 
current flows in the upper half of the circle from south to 
north. Enter your conclusion in your journal. 

407- Xow perform the experiment yourself with a cov- 
ered wire conductor forming a circle, and provided with a 
magnetized sewing needle, suspended by a silk string, at- 
tached with sealing-wax (see fig. 45) : be careful to bring 
the plane of the ring in line with the direction of the 
needle, before sending the galvanic current through the 
wire ! Record the result and compare it with your con- 
clusion (406). 

408. What will be the effect on the needle of having 
the same current pass through several such circular wind- 



144 Chapter V. 



ings of the same conductor? Test 3 r our conclusion by an 
experiment with such a conductor. State results in your 
journal. 

409. If different currents are successively sent through 
the same wire, wound as described in 408, the deflection 
ot the needle will be different for the different currents. 
Hence such an apparatus may be used as galvanometer 
the deflection in degree,? of the needle serving as index of 
the strength of the galvanic current. It is, of course, es- 
sential that the plane of the circular conductor coincide 
with the direction of the needle before sending the cur- 
rent through the wire. 

410- The simplest galvanometer, fig. 46, is made by 
winding a cotton or silk insulated copper wire (1 to 2 mm. 
diameter) around any cylinder (about 1 dm. in diameter) 
and then binding the windings by one additional course 
of the wire wound around the coil. The coil may be fas- 
tened vertically to a square piece of wood (1 dm. side, 3 
cm. thick) to which the extremities of the wire are firmly 
attached by staples of copper wire driven into the wood. 
By means of a cork and sealing-wax a divided circle of 
card paper is fixed with its plane horizontal and its center 
a little (3 mm), below the centre of the vertical coil. 
From the upper point of the co^l a magnetized sewing 
needle is suspended by means of a fine silk thread (see 
313) so that the centre of the needle coincides with the 
centre of the coil. 

Before use. turn the wooden support until the needle 
coincides with the diameter marked zero on the divided 
circle — this diameter being determined by the plane of 
the vertical coil. The degrees are numbered each w x ay 
from zero to 90 degrees. The deflection in degrees, will 
then give an approximative measure of the strength of 
the current. 

411. The strength of the current is, however, not pro- 
portional to the number of degrees which the needle is 
deflected, but grows at a much more rapid rate than the 
number of degreed. This will be studied in the Principles 
of Physics. Here it is enough to know that the strength 
of the current is the same for the same angle of deflection, 
and greater for a greater angle of deflection. 



Electro-Magnetism. 14 5 



412. If instead of a few windings of stout copper 
wire, as used in the galvanometer (410), we use many 
windings of very thin silk-insulated copper wire, the ap- 
paratus is called a galvanic multiplier or a galvanoscope. 
It will no longer serve as a measure of stronger currents, 
but be excellent as an indicator of very feeble currents 
and their direction. 

413. The Needle Telegraph. — If a small galvanic 
cup be at one station, A, and a mupltiplier at another sta- 
tion, B, connected with A by means of a metallic con- 
ductor, then a. galvanic current may be sent from A along 
the conductor to B, through the multiplier at B and back* 
to A. 

414. By changing the connections at A, the current 
may be sent so as to deflect the needle at B either to the 
right or to the left of the observer at B. If now a sign 
alphabet, composed of right and left deflections of the 
needle, has been previously agreed upon, A may, by pro- 
ducing the proper deflections at B, transmit these symbols 
of letters, and thus transmit entire words. 

415. This is the principle of the needle telegraph, so 
much used in England. The same, but in a considerably 
refined form, is used for working the oceanic cables be- 
tween Europe and America. One small cup, like the one 
described above, gives sufficient power to transmit a dis- 
patch from one continent to the other ! 

416. If the current sent through the coil of a galvanic 
multiplier "te strong, f the magnetic needle will stand 
very nearly at right angles to the plane of the coil. 

417. If you now suppose yourself standing on the 
south pole of the needle and facing the coil, the current 
in the latter will flow around you from left to right, ex- 
actly as the hands of a watch move over the dial-plate. 

♦Usually through the earth ! 

fThat is produced by zinc and copper plates of considerabie size — say 100 square 
centimetres each. 

19 



146 Chapter V. 



When you stand on the north pole of the needle, the cur- 
rent flows apparently in the same direction. 

418- Hence we must conclude, that as the galvanic coil 
acts like a magnet, the south pole of lohich is that end of 
the coil ivhere the current appears to flow in the direction 
of the hands of a watch, to any observer standing on that 
end of the coil, the opposite end of the r coil will be the 
north pole. 

419. This conclusion is correct, as may be verified by 
De la Rive's floating current and by the magnetizing coil. 

The former is rather troublesome to manage. Hence it 
may be sufficient here to demonstrate the above conclusion 
by means of the magnetizing coil. 

420. A magnetizing coil may be made by winding a 
copper wire on a glass tube (2 to 10 mm. internal diame- 
ter). If now the galvanic current be passed through the 
coil while a small non-magetized sewing needle lies in the 
middle of the coil, the needle will soon be found to have 
become magnetized. 

421. Experiment with such a coil connected with a 
rather large galvanic element. Magnetize a sewing needle, 
and carefully ascertain whether its poles are formed in ac- 
cordance with the law stated in 418. Also, insert a piece 
of soft iron into the coil ; ascertain its magnetic power 
(303) and polarity (321) in the usual manner, while the 
iron is in the coil, and after it has been taken from the 
same. Also, experiment in the same manner with the coil 
itself. Carefully observe, and record your observations 
in your journal. 

Also, answer the following : Could the magnetic force 
of the earth be produced by a galvanic current around the 
earth ? In what direction must the current flow as com- 
pared to the apparent daily motion of the sun ? 

422. An electro-magnet is a piece of soft* iron, sur- 
rounded by a coil. While a galvanic current passes 

♦To make sure of this, the iron must be reheated to redness after having been 
fashioned, and then left to cool gradually. If the iron is not quite soft, some mag. 
netism wiil always remain in it — the residual force. 



Electro-Magnetism . 147 



through the coil, the electro-magnet is excited ; this is also 
expressed by saving the electro-magnet works or is mag- 
netized while the circuit is closed. It will have no mas:- 
netic power while the circuit is open. Compare the re- 
sults of your experiments 421. 

423. Electro-magnets are very generally used. In 

>rm they are most powerful. Compare 301 and 
302. Some electro-magnets hold their keeper with a force 
of more than a ton. 

424. The principal applications of electro-magnets are 
in the electro-magnetic telegraph and in electromagnetic 
motors (machine 

425. The Morse- Tel 'eg raph* depends upon the magnet- 
ization of iron at a distance by a galvanic current sent 
along the telegraph wire. At the speaking station A, tig. 
47. is a strong galvanic battery. By pressing the key K, 
the circuit is closed and the current passes along the tele- 
graph line to the receiving station B. and back through 
the earth (compare 113). At the station B, is a small 
electro-magnet AT. the coil of which forms part of the cir- 
cuit. Hence, while the circuit is closed (at A N ) the electro- 
magnet M is excited, and attracts the keeper K' (302 x ) held 
by means of a spring, at a very small distance from It 

426- This minute motion of the keeper K 1 . is by means 
of a galvanic battery at B, (the local battery) and an 

itionai electro-magnetf (the receiver) made apparent 
either to the eye or to the ear of the telegrapher at B. 

427- The effect produced being simply the magnetiza- 
tion of the electro-magnet M 3 of the relais (and receiver) 
the alphabet used must be composed of long and short mag- 
netizations, produced at will at the speaking station A by 
pressing the key K down for a longer or only for a shorter 
time. Thus in Morse's alphabet the letters consist simply 
of -longs- and -shorts/ 4 

inheil used the same principle. 
fThe first electro-magnet at B is called the BeUas. See M in 



148 



Chapter V. 



428. Usually, a long line of telegraph, 800 to 1000 
kilometers, is run by one strong battery of about 100 Bun- 
sen or Grove elements (399) at the central station. The 
way stations have only the local battery for their receiver ; 
also, a key for speaking and a relais for receiving dis- 
patches. 

Thus on the line from Chicago to Council Bluffs, there 
is only one strong battery (at Chicago), working the wire. 
Between New York and San Francisco, only four or five 
such batteries are in activity. 

429. If the keepers K and K 1 of two strong elec- 
tro magnets M and M l are attached to the opposite 
extremities of a line, the latter will alternately move its 
arms up and down, as the current is sent alternately 
around M or M 1 . Then this lever may be made the walk- 
ing beam of a machine and be applied for all sorts of me- 
chanical work. Such an application is termed an electro- 
magnetic motor, or less properly electro-magnetic machine. 

430. Electro-magnetic machines have been constructed 
strong enough to move a train of cars on a railroad, (Page, 
near Washington) or a boat on water, (Jacobi, on the 
Neva, near St. Petersbnrg). 

But mechanical work costs thirty to forty times as much 
per horse-power when produced by an electro-magnetic 
machine than when produced by a steam engine. Hence 
the electro-magnetic machines have no practical import- 
ance. 



VI. INDUCTION. 



431. A piece of soft iron in contact with a magnet, is 
magnetized strongly while thus in contact (305). But even 
if the soft iron is held at some distance from the magnet, 
it will already be distinctly magnetized. As the magnet 
again recedes from the iron, the magnetic force in the lat- 
ter is again diminished. 



Induction. 149 



432- The action of a magnet on soft iron at a distance 
(great or small) is called magnetic induction and the 
magnetism thus produced in the softer iron is called in- 
duced magnetism. 

433- An electrified body approaching a good conduc- 
tor also electrifies the latter ; the electricity produced is 
called induced electricity, and the action is termed elec- 
trical induction. The action also increases greatly in in- 
tensity as the distance diminishes. 

434. A further study of the phenomena and laws of 
induction must be reserved for the principles of physics. 
Here it is only necessary to refer to the motions produced 
by induction. 

435. The motion of a piece of iron suspended like the 
electrical or magnetic needle upon the approach of a mag- 
net, represents a certain amount of mechanical work due 
to magnetic induction. Hence, inversely, magnetic induc- 
tion must be the result and the equivalent of a correspond- 
ing amount of mechanical work. 97. 

436. An electrified body brought near an easily moved 
neutral body, causes the latter to move (342 and subse- 
quent). At the same time electrical induction takes place, 
as that the latter must be considered the equivalent of the 
mechanical work of the motion. Hence also motion again 
should produce electrical induction. This is most striking- 
ly confirmed by Holtz's electro-machine, 379. 

437. In general, magnetic or electric induction results 
in the exhibition of mechanical work, and mechanical 
work applied to proper apparatus, yields magnetic or elec- 
tric force. Compare 97. 

438. Since magnets and galvanic currents mutually 
act upon each other (section V.) the above general prin- 
ciple ought also to be applicable to galvanic phenomena. 
That the galvanic current by magnetic induction in the 
electro-magnet and its keeper produces mechanical work, 
has already been shown (see 429 and 430). By reversing 



150 Chapter V. 



such an electro magnetic machine we should therefore be 
able by the application of mechanical work to produce a 
galvanic current. 

439. The magneto-electric machine confirms this con- 
clusion. Here mechanical work is applied to rotate several 
coils of fine copper wire between strong magnetic poles 
— and very intense galvanic currents result. 

The full study of the details of such machines belongs 
to the principles of physics. The teacher, may, how- 
ever, exhibit such a machine in action before the students, 
so that they may become cognizant of the fact that mechan- 
ical work is transformed into galvanic currents by such 
machines. 

440- Siemens, of Berlin, has constructed very power- 
ful coils of this kind. By the Englismen Wild, in 1865, 
and by Ladd, somewhat later, these coils have been com- 
bined to most effective machines of this kind. These ma- 
chines, when turned by a steam engine, produce a gal- 
vanic current of greater strength than a Bunsen battery 
battery of several hundred large elements. 

441- Since a magnet may be replaced by a coil through 
which passes a galvanic current (421) it follows that no 
magnet is required to produce a galvanic current by in- 
duction, but that another current will suffice. Such in- 
duction of a galvanic current is often termed volta-induc- 
tion. 

442. The simplest mode of volta-induction consists in 
closing a circuit of thick, not too long wire, just for an in- 
stant, in the neighborhood of a long coil of thin wire. 
The latter will thereby be pervaded by an intense induced 
current. 

A few experiments on this kind of induction may be 
performed before the students. The more detailed study 
of this subject must also be deferred to another course. 

443- If the inducing coil contains soft iron wires, the 
latter will be magnetized by the inducing current, and 
thus magnetic-induction will be added to volta-induction 



Conclusion. 151 



in the induced coil. The induced current will therefore 
be greatly intensified by soft iron wires in the induced 
coil. Also this fact may be readily exhibited to the 
students. 

444. The simplest way of exhibiting the presence of 
induced currents is by their effect on the muscles and 
nerves of the body. By taking hold* of the metallic 
handles attached to the extremities of the induced coil, a 
shock will be felt, each time the inducing circuit is closed 
and broken. The latter gives the most intense shock. 

445- The galvanic current, as produced from one or a 
few elements, is hardly felt when passed through the arms. 
But the same current used as inducing current with a fine 
induced coil, produces an induced current which gives a 
powerful shock, especially if soft iron wires have been in- 
serted in the inducing coil. 

446. Light and heat are also produced by the galvanic 
current direct, as well as by the induced current. By means 
of a powerful galvanic battery, the brilliant carbon light, 
also termed the voltaic arch, can be produced. Sparks are 
readily produced when galvanic currents passing through 
coils are suddenly interrupted, as will be seen at most ex- 
periments with induced currents. 

447. All of these phenomena must, however, be de 
ferred till the next higher course in physics, when the 
principles of this branch of physical science can be more 
fully considered. 

VII. CONCLUSION. 

448. The cords, levers, supports, and pulleys, in the 
mechanical powers (see chapter II.) can only transmit 
mechanical work, not create any. Compare especially 87. 
The peculiar electric and magnetic phenomena are, accord- 
ing to the preceding, only more delicate cords and levers, 

*Especially with hands moistened with salt water to increase the low conductiv- 
ity of the skin. 



152 Chapter V. 



by means of which mechanical work can be transmitted. 
We shall give one or two examples. 

449. The mechanical work applied to tnrn the electro- 
machine (379) produces an abundance of electricity, which 
may be used to yield light, heat, shocks, etc.; but it may 
also again be applied to light bodies, which thus will be 
brought into motion, so that the original mechanical work 
reappears. 

Mechanical work applied to a magneto-electrical ma- 
chine (439) produces an induced current, which again may 
be changed into light, heat, shocks, magnetism, etc. ; but 
the current may also again be applied to an electro-mag- 
netic machine (429, 430) and thus reproduce mechanical 
work. 

In both these cases mechanical work apparently had 
completely disappeared ; we received only magnetism, 
heat, light, electricity etc., which at first sight appear total- 
ly different from mechanical work. But these various 
phenomena are evidently merely mechanical work in dis- 
guise; at any rate, it is in most cases quite easy to repro- 
duce the original form of simple mechanical work. 

450. A complete conversion of one form into another 
is quite difficult ; hence it requires very careful determin- 
ations to prove that the absolute amount of mechanical 
work remains unchanged in all these forms, as indicated 
in the general equation in 87. Mayer, Joule, Helmholtz, 
Ilirn, and many others have (see 97) proved by careful re- 
search that the amount of mechanical work really is a con- 
stant quantity in nature as well as the amount of matter 
itself! 



GUIDE TO THE PEOPER STUDY 



OF THE 



ELEMENTS OF PHYSIOS. 



L INTRODUCTION. 

451» By means of our senses we recognize a multitude of diverse things, bodies, or 
objects around us. The totality of all that can thus be recognized is called Nature 
Universe, Cosmos, or Physis. That, which exists, and constitutes these things, is 
termed matter or substance. 

452* What is ascertained (made certain), concerning these existing things is termed 
science. It therefore excludes all mere probabilities, fancies, and suppositions. 

453. In the study of science, certainty is often obtained through the develop- 
ment and consideration of probabilities and suppositions (often termed hypotheses). 
These latter are therefore treated of in Higher works on science; but they should 
always be represented, not as legitimate and constituent parts of science, but as 
mere accessories and instruments for further study and consideration.* 

454* Hence, no hypotheses should be referred to in the mere elements of sci- 
ence. The beginner should, first of all, become accustomed to the certainty of scientific re- 
Suits. Then he will afterwards be able to weigh the value of hypotheses for himself. 
The discussion of hypotheses in elementary works ie a remnant of a barbarous meta- 
physical age, and cultivates the same looseness and muddyness of thought and 
reasoning for which that age is noted. f 

*The general neglect of scientific study accounts for the popular falacy of " revolu- 
tions " in science, and like absurdities. Science knows only of progress and development; 
it continually penetrates deeper and wider into nature. 

Speculation changes. Hypotheses rise, and either become part of science, if found 
true, or pass into oblivion. 

fAs an example we add Aristotle's demonstration that the earth is in the center of the 
world, as given in the famous Treatise on the Heavens (II. 3,1), of that philosopher, 
whose authority was supreme until Galileo, the founder of modern (physical) sci- 
ence, proved the emptiness of such metaphysical speculations. The extract here 
following is also printed to serve as a warning to the students and teachers against 
verbiage, loose speculations and metaphysical pretentions. Aristotle demonstrates 
thus • — 

" Everything which produces a certain act is made in view of that act ; now the act 
of God is immortalicy ; in other words, it is an eternal existence; therefore it is nec- 
essary that the Divine have an eternal motion. But the firmament has that quality, 
because it is a Divine body; and therefore it has th e spherical form, which by its 
nature moves eternally in a circle. Now how does i: happen that the entire body of 
the firmament is not thus in motion? It is because it 3e3sarily, one part of a body 
which moves in a circle, keeps its place and remains sl\ rest ; and it is that part which 
is at the center. For the heavens, it is not possible that any part remain immova- 
ble, or anywhere, or at the center, for then its natural motion would be towards the 
center ; and since its natural motion is circular, its motion from that instant would 
no longer be eternal. But nothing which is contrary to nature can continue forev- 
er. Now that which is contrary to nature is posterior to that which is according to 
nature; and in the order of generation, that which is contrary to nature is but a de- 
viation from that which is natural. Therefore it is necessary that the earth be in 
the center and that it remain there at rest. But if this be so, it is necessary that fire, 
which is the opposite to earth, should also exist. Further, affirmation is anterior to 

20 



154 Guide to the Study of the 



455. Science proper, free from all hypotheses and speculation, is amply suffi- 
cient any diligent student engaged for years. Therefore again: the ele- 
ments of science should be restricted to science proper (452). 

456. Science, as defined above (452), leads constantly to applications useful to 
society; hence it is proper, in the elements to refer to noted examples of such appli- 
cations. Modern civilization differs from all other stages of civilization, mainly by 
the thorough research in and the astonishing applications of science. Examples: — 
Clocks, telegraphs, steam engines, railroads, iron and steel smelting in mass, prepa- 
rations of splendid colors from tar, etc., etc. 

45 7. A multitude of bodies possess parts performing definite functions, at least 
for some tiaio ; such parts are termed organs, and the bodies themselves organic bod- 
ies. 

458. That branch of science which treats of organized bodies (plants and ani- 
mals), is termed Natural Science. The investigators in this field of science are termed 
Naturml\8ts. Tho remains of plants and animals found in rocks are also treated of 
in natural science (paleontology). Other branches of natural science are zoology, 
botany, physiology, anatomy. 

459. That branch of science which treats of matter, in general, irrespective of 
special organs, constitutes physical science. It therefore treats of all bodies desti- 
tute of organs (rocks, minerals, air, water, chemicals, and other products of human 
industry; also, the sun, the moon, and the stars). Rational physiology is a branch 
of physical science now rapidly being developed by careful research. 

460. Physical science is most conveniently divided into three branches: Phy- 
sics. Chemistry, and Cosmos. Physics treats of magnitude, weight, motion of bodies, 
of light, electricity, and magnetism. Chemistry* treats of the changes of bodies by 
heat and intimate mixtures. Cosmos treats of the physics and chemistry of the lar- 
ger bodies in the universe, namely: the sun, moon, and stars, and also, the earth, the 
sea, and the air, considered as a whole, 

461. The elements of these three branches of physical science will be treated of 
in three separate volumes, namely: — 

I. The Elements of Physics. 
II. The Elements of Chemistry. 
III. The Student's Cosmos. 
The following is a short guide for student and teacher to this, the first volume. 

II. THE FIRST CHAPTER 

462. Most works on physics give lengthy considerations of, sometimes, as many 
as ten general properties of matter. Of these we retain only extension or magnitude, 

privation, I mean to say for example, that heat is anterior to cold. Now rest and 
gravity cannot be understood but as the absence of lightness and of motion. But 
> t h and fire do exist, ihen it follows, necessarily, that all bodies intermediate be- 
tween tho-. ; two exist as well as they, for each one of the elements must have its 
contrary which is opposed to it. These elements existing, it is absolutely necessa- 
ry that they hi treated. These bodies which we have just named are en- 
dowed with motion. From this we, therefore, see clearly the necessity of the motion 
of general ion ; and from ihe moment that generation exists, it is also necessary that 
there be • I a of motions, lie they one or many. We see clearly by what cause 
bodies subject to a circular motion are more than one. It is because there necessar- 
ily must be generation; and there is generation because there is fire; and fire exists, 
as w ■!] is the other elements, because the earth also exists; finally, the earth itself 
exi be one body which remains forever at rest, since there must 
be eternal motion." 

aft-r no one will doubt the conclusions so clearly established by 
the greatest master of classical Greece. If any doubts remain, just read this dem- 
onstration once more. 

*The elements of chemistry wfU properly include the elements of mineralogy, as the 
science of the chemical compounds found in the earth as minerals. Also, a descrip- 
tion of the principal rocks. 



Elements of Physics. 155 



for all the other so-called general properties of matter are simply metaphysical spec- 
ulations and abstractions, remnants of a pre-scicntific day. 

463. These numerous so-called general properties are, moreover, commonly of- 
fered to the beginner as the very first step in science; these properties are "illustra- 
ted " by experiments, for being speculations they cannci be demonstrated. Thus a 
radically false step makes, bat too often, the beginning in physics. 

464. Weight is usually not given by books as a general property of matter ; but 
it is truly so, — the so-called law of universal attraction proves it. 

465. Since now weight and magnitude are general properties of matter, we must 
commence the study of matter with the study of these two properties. Measuring 
and weighing are, in fact, the corner stone of physical science. This should be dis- 
tinctly understood, so that the chapter is studied with due attention. 

466. But not only in science— also, in civil life, magnitude and weight are of 
fundamental importance. Almost all business transactions, all trades, ultimately 
rest upon weight and measure. Let the students enumerate special branches of 
business, using measure of length, of area, of volume, of weight, singly, or any two 
or more combined. 

467. In actual business transactions, these magnitudes and weights are inter- 
changed according to the magnitude or weight of some conventional material, adopted 
as the standard of value. As such, the precious metals gold and silver have been 
usedf from time immemorial. 

468. To facilitate interchange, the government does the weighing of the precious 
metal for the people, and stamps the true weight of pure metal upon the several 
pieces formed in the shape of coin. Thus the number of pieces need ocly be coun- 
ted, in order to know the amount of the metal in weight. 

469« The truly rational coin would be a gold coin containing a definite and simpis .lum- 
ber of grammes of gold. The United States double eagle, or twenty dollar gold coin, very 
closely approaches this requirement, for it does contain 30.0906 grammes of pure 
gold, that is very little above thirty grammes fine gold. 

470. The value of silver, in regard to gold, changes in time according to the yield 
of the mines and other circumstances. It is therefore absurd to adopt, by law, both 
a gold and silver standard. Notwithstanding, it has been done by most govern- 
ments. 

471. The weights, measures, and coins, in actual use in most countries, are the 
remnants of a crude state of civilization and are, therefore, mostly in flagrant opposi- 
tion to the principles of science. This is most emphatically the case with the Eng- 
lish system, as the teacher may show by reference to the tables given in arithmetics. 
Unfortunately the people of the United States adhere to this "system" with even 
greater tenacity than the English, who are ready to become ashamed of using it any 
longer. Compare 3 and 4. ^ 

472. The continued actual use of these absurd and barbarous "systems" imposes 
upon us the reduction of one to the other. In practice this reduction is performed 
by means of factors or tables, as explained in the appendix to this volume. 

473. We cannot too emphatically protest against the remnant of a crude stage of 
civilization or even barbarism represented in the English system of weight, meas- 
ure, and coin. The great length of time spent by every child at school, on reduction, 
is that much time worse than wasted — it represents an incalculable loss of life to civ- 
ilization. That much time properly devoted to science would soon yield rich fruits to 
society ! 

fBoth gold and silver are too soft for use, when pure ; hence they are alloyed with 
copper to harden the coin sufficiently. The United States coin contains ten per cent 
of alloy, and ninety per cent of fine metal. 



156 Guide to the Study of the 



III. MENSURATION. 

474:. Articles 41 to SO, inclusive, are considered most important, because, as sta- 
ted On 40\ the mathematical instruction, in our schools, does not give the students 
this practical preparation. 

475. It is, however, but just to admit, on our part, that especially the section (V.) 
on mensuration, is not mathematics proper, but constitutes the simplest possible in- 
troduction to the methods of physical research. We also think that it should pre- 
cede the study of pure (abstract) mathematics. 

476. Accordingly, we insist on each student carefully working his way, at least, 
through articles 41* and 42 ; giving especial attention to the explanations in 42. The 
student should work as many more of these exercises in mensuration as time and 
circumstances will admit, always, at the close of each exercise, again carefully study- 
ing article 42. 

477. In connection with this practice in mensuration, the beginner will learn 
why the physical sciences are often termed the exact sciences. Not that any quantity 
can be determined with perfect accuracy, but because in this science we can determine the 
very degree of accuracy attained. Compare 31. 

478. The student, who works with care some of these exercises on mensuration, 
will have acquired some degree of culture in his fingers, so very necessary in exper- 
imentation. Nothing used in these exercises is easily damaged ; hence good prac- 
tice is acquired, without risk of breakage. 

SKETCHING. 

479. The teacher should insist that the student draw the sketches, spoken of in 
43, 44, and 45, by/reehand, without the aid of any ruler whatever. Only by com- 
mencing with such simple sketches will the student, in time, be able to draw the 
more difficult sketches required farther on in the book— and acquire an art so very 
useful in any position in actual life. For the proper drawing of the sketches of sol- 
ids in 44, the student should carefully consult 75, especially the last paragraph. 

In connection herewith, it is important to notice, that lines which are parallel in 
the object, must be parallel on the sketch. Also, that any circle is determined by 
two of its diameters. If the circle be horizontal, the diameters parallel to axes X and 
Y are drawn by finely dotted lines, and an oval is drawn through the extremities of 
these diameters. 

In the study of the subsequent chapters the student should always enter a sketch 
of the apparatus he experiments with, in his journal, together with the careful rec- 
ord of his experiments. If this is insisted upon by the teacher, the student will 
soon thank him for it. The student will, in this manner, also become more thorough- 
ly familiar with the construction of the apparatus, than in any other way. Thus 
the precise form of batteries, balances, microscopes, telescopes, etc., etc., used by 
the student, should be represented by the sl^tches in his journal. 

All sketches are free-hand dravnngs, and shoula consist of fine, light, pencil-lines; elegance 
as well as truth (correct position and proportion), should be constantly aimed at. 

To give the class a proper start, the teacher should have the students study 75 to 
78, then practice the subject by drawing a sketch of a simple apparatus on the black- 
board before the students. The apparatus should be placed so that all students sit 
*0 the right and above the apparatus— while the teacher, with the constant direction 
of tho el; ketch on the blackboard. In this manner the students 

readily become familiar with this work, and will perceive both the utility and beauty 
thereof. 

Any teacher not yet able to do this, should lose no time, but begin at once to 
learn. No one is fit to teach, who cannot draw a sketch of simple things. 

•"Pieces of glass rod form the most elegant set of models for 41. 



Elements of Physics. 157 



IV. LINEAR DRAWING. 

480» Each student should, most carefully, work his way through all these ex 
ercises ; but no one should continuously be engaged in this work, on the contrary, 
each student should only spend a few hours from time to time at linear drawing, so 
that for each student the exercises in drawing regularly alternate with the experi- 
mentation proper. In this manner each student may complete articles 51 to 64, 
during the first quarter, from 65 to 74. during the second quarter v and from 75 to 80, 
during the third quarter*— thus completing this very elementary course in linear 
drawing, in a school year of about nine months. 

In this manner the work of the student becomes diversified, and the school may, 
with a limited apparatus, accomplish a great educational work. 

481. No part of this elementary work is more difficult, than this section on lin- 
ear drawing." Our teachers are, as a rule, themselves unable to draw a straight line; 
a chalk line on the blackboard is, by too many of them, considered a line, indeed. 
I therefore make a few additional suggestions which all should most scrupulously 
heed, who wish to draw or to teach linear drawing. 

1. Be sure to sharpen the 'pencil as directed (footnote, page 26): without doing 
this, you need not attempt to draw, for it will be impossibfe. Reserve this point of 
the pencil for drawing exclusively. If No. 3 pencil is still too soft, buy a No. 4. 

2. Hold the pencil precisely as directed in 52. »Let the lines be just simply dis- 
tictly visible, and no more; a ]ong mark 1-5 mm thick is no longer a line, but a 
stroke, a beam, a broom stick. But at the same time have the line equally heavy 
throughout its entire length. Its margin sharp. 

3. Mark points precisely as described in 54. Do not stop a line at a point, but car- 
ry it beyond at once while drawing the line: only in that way can you obtain a real 
peint marked by the crossing of the lines. This is especially important when the 
angle is afterwards to be measured by a protractor (56). Draw the small circles by 
free hand, very fine, and sufficiently far from the point so as to leave the latter free. 
Never press the pencil on the the point, much less rub some graphite on what was a 
point, but thus becomes a coal pile. The teacher should be strict in regard to these 
matters, and permit no one to pass on, unless the exercise has been performed 
neatly and accurately. 

4. The blank paper in the journal of this volume is quite well adapted to draw- 
ing, if only the book is properly folded out ; hence no extra drawing paper (see 52) 
need be procured for common work. 

5. The dividers should, almost exclusively, b© handled by holding the knob be- 
tween the thumb, first, and second fingers, of the right hand. The points should 
but gently press against the paper; distinctly touch the paper, faintly mark it, no 
more. 

6. Only by taking these exercises quite serious from the first, can the student be 
benefited by them. iVo drawing, not carefully and accurately done, should be recognized 
by the teacher, for it is useless. He should^ however, himself be able to show the stu- 
dents, by a few lines, that accuracy can be attained. Excellent and simple test of ac- 
curacy is 58. The error should not be greater than 0.005. 

7. Whenever lettering is required, the simple Roman or gothic capitals should be 
used, in preference to script. The student should take especial pains to avoid all 
flourishes. 

8. Beginners are often tempted by the drawing pen. The teaeher should inform 
such, that it will take at least a year to be able to handle the pencil as it should be — 
so that the drawing pen will not be used the first year. 

9. Students often are anxious to purchase a case of drawing tools. They should 
be dissuaded from that, unless they are ready to spend at least fifteen dollars. The 
cheap boxes are good for nothing to any one who wishes to produce accurate drawings. 
We recommend simply the instruments enumerated in 51; No. 3 and No. 4 may be 
bought together, of good quality, for about one dollar. Examine the hinge and the 
points of the dividers, before you purchase. 

10. Good drawing tools should of course only be used for actual drawing. Be- 
ware, therefore, of handling these tools, except while actually using them for draw- 
ing. 

♦This will include drawings to scale oi some, not too intricate apparatus, such as 
a telescope on stand, etc., etc. 



158 Guide to the Study of the 



V. THE SECOND CHAPTER. 

4:82. This chapter* is comparatively difficult. However, if the students are not 
sufficiently prepared to work their way through this chapter, as it stands, the deduc- 
tions may first be omitted, and only the experimental demonstrations given, espec- 
ially those in 90, 92, 95. 

4:83. For this purpose only, 81 to 87, need first be mastered. Then each student 
should experimentally determine the simultaneous values of P, H, p, and r, as dir- 
ected. He will then always find that the general equation in 87 is satisfied, giving 
but a small value of the internal work I. 

484:. This may be the proper place to state, that the study of algebra is not re- 
quired in order to understand this or any other chapter of these elements. The 
explanations in 41 and 42, together with the constant use of initials to denote the 
diil'erent quantities, will enable any student to use these symbols as directed— and 
as done in algebra, proper, to which just such work ought to form the stepping 
stone. 

485. From 97, it will be seen how important it is that this second chapter should 
be studied well. All the multiform machines used are merely special cases of 87 and 
88, and combinations of the simple machines 89. The student should, himself, study 
some one machine in this regard; carefully work the problems given on this subject. 

486. We shall also, add a few interesting facts — without, however, here at- 
tempting to demonstrate the same. We shall, merely, give the name of the investi- 
gator who has ascertained these facts. 

lite interior work of a man is at least 100,000 kilogramme-meters per day. 

For, according to Helmh.oltz and others, the mechanical work of circulation is 70,000, 
that of respiration 11,000 kilogramme-meters, 81,000 for circulation and respiration 
alone. The above estimate leaves, therefore, only 19,000 for the other processes. 

The external work, or the work overcome by a man, in external resistance, may 
also be taken at 100,000 on the average (compare 86). 

Hence, the active human body can, each twenty-four hours, perform a mechanical 
work of 200,000 kilogramme-meters, half of which is required internally to keep the 
organs of the body itself in action, while the other half appears as external mechan- 
ical work actually done by the man. The power applied is the food. It will easily 
be unders'ood why food is required each day. 

In a good steam engine,! each kilogramme of coal burnt, produces a mechani- 
cal work of about 300,000 kilogramme-meters. Hence, we may say that the combus- 
tion of one kilogramme of coal is equivalent to the mechanical work of three men for 
one day. 

Why, then, is the labor of a steam engine cheaper than the mechanical labor of 
man? 

* Here, for thp first time theoretical demonstrations enter. The law of equilibri- 
um of each machine is demonstrated both by theory and by experiment. 
By theory, or mathematical deductions from some more general theorem; in 93, 
d of equilibrium is deduced from the law 87 (89) valid for 
machines. Notice ihat no loose reasonings are admitted, but only strictly math- 
ical deduct". 
theoretical dem< I however, not sufficient to fully establish a phy- 

sical law. the demonstration by theory must always be added the demon- 

riment, as hai been done in the U xi. 

■ of the clase ia not high enough to master the theoretical demon- 
ion, let tli ite the laws by experiment and see that all sim- 
ple machines lead to 87. Suc1< a process, from fact to general principle, is termed 
-on. 

fCo ; 



Elements of Physics. 159 



VI. THE THIRD, FOURTH, AND FIFTH CHAPTERS. 

487. These chapters will, perhaps, generally be found easier than the second 
chapter. Hence, we need not here enter into any details about the study of the 
same. If only the subject is first presented by the teacher to the students, who 
should already have read the lesson assigned ; if then the students practice a 
sufficient number of the experiments under proper personal supervision of the teach- 
er— they will really understand the subject, and be able to pass a rigid* exam- 
ination. The student thus, also, can solve the simple problems appended to this 
volume. 

• Only a few points need special additional remarks here. 

488. In 123 the method given should be used to determine the specific gravity 
of some solids, especially, if a balance weighing to the centigramme, be at hand. 

489. The subject of sound seems very meagerly represented (see 141 to 143). 
Still these few paragraphs contain really more than many large manuals of physics 
on the same subject. A detailed study of wave motion, belongs to the principles of 
physics. 

However, if apparatus be at hand, the teacher may amplify ; but if no additional 
apparatus is at service, the students would better spend their time as directed. 

We would recommend the teacher to exhibit, in connection with 143, the nodal 
figures of a square glass plate, of which the edges have been ground off. 

490. In optics, mirrors have received no special attention. Plane mirrors are 
familiar; curved mirrors, which really will show good images, are far too expensive. 

Hence, it is quite enough, if the attention of the students is called to the facts, that 
in plane mirrors the (virtual) image is symmetric with and equal in size to the ob- 
ject; and that convex mirrors give, always, diminished, erect, and imaginary im- 
ages, while concave mirrors correspond to convex lenses. 

The outer curved surface of convex lenses shows the images of convex mirrors. 

VII. THE SCHOOL LABORATORY. 

491. The practice given in these elements of physics may be divided into desk- 
work and table-work. 

Desk-work, to be performed by the student at his deskf is: Chap. I. Sees. 5 and 6; 
Chap. III. Sees. 4 and 6; Chap. IV. Sec. 1. 

All the rest is, essentially, table-ivork, that is, it must be performed at some work- 
table, specially fitted up for the purpose and provided with the necessary apparatus. 
For most schools, a walnut-stained pine-wood table, about eighty-five cm. high and 
sixty cm. wide, running along one side of the school room, may be sufficient. 

The students at work at the tables should stand, never sit down. 

The balances should be permanently located at such places as are of convenient 
access to all students. At least two balances are required, one for weighing smaller 
bodies (mensuration, specific gravity, etc.), and another for determining weights up to 
one kilogramme (chapter II). 

*We cannot too strongly urge the the teacher to give honor to whom honor is 
due. If a large class grade, at the close of a term's work, from 95 to 100 — it shows, 
simply, that the teacher is unable or unwilling to discriminate. In a class of about 
two hundred, studying these elements, we gave only four students 100 (the highest 
value), because the work was done as good as possible for that grade. About ten 
other students in the same class ranged from 05 to 99. All the others fell below 95. 

To mark a careless, slothful student as high as a diligent one, and the latter as 
high as those who work, not only with diligence, but also with energy and delight, 
does exert a thoroughly bad influence on the intellectual condition of the school. 
It is, however, often quite popular. 

-j-Our common fancy desks are not the most practical. Plain, walnut-stained ta- 
bles, with like seats, made by any good carpenter, and arranged on a rising platform, 
constitute a vastly superior school furniture. The top of the desk should be level. 



160 Guide to the Study of the 



492. The apparatus required for that portion of the book which is being studied 
by the class, should be permanently placed on the work-table. The drawing tools, 
models, and specimens, for the desk-work should be kept in small trays near the 
desks. The students at tho table pass from one apparatus to the next, ae> they have 
finished the experiments. 

As soon as all have performed the necessary experiments with a given apparatus, 
it may be removed from the table, and replaced by another. 

493* It will readily be perceivod, that a separate room for work is not absolutely 
necessary, but that it is exceedingly desirable. If all classes meet in the same room, 
there will be more dust,* and it will be more difficult to keep every piece of appar- 
atus and every specimen in its proper place and condition, than when all practical 
experimental work (labor) is performed in a separate room, called ta© Laboratory. 
Each teacher should aim to get, at least one good room set aside to be used exclu- 
sively as a school laboratory of physical science. 

4:94:. Under the work-table may be cupboards for keeping apparatus and spec- 
imens. Or better still, a small cabinet room, adjacent to the laboratory, should be 
set aside for the reception of all apparatus not in actual use. 

495. Another point of great importance is the proper labeling of the specimens 
and apparatus. The simplest system of such labels is that of double numbers. 

The first number on the label gives the number of the articles in the book. The 
second number on the label gives the number of the piece used in that article. If 
for any article, several sets of apparatus are in use, distinguish these sets by the 
letters a, b, c. 

These numbers are again given on a card, together with sufficiently plain descrip- 
tion of the object. The contents of all cards may be recorded in a catalogue. The 
student obtains the card, together with the apparatus enumerated thereon; it is his 
duty to see that he obtains all that is mentioned on the card, and all in good order— 
for it is the teacher's duty, in regard to the school, to see that the student faithfully 
returns all that the card enumerates, and all in perfect order. These cards thus 
form a check for both student and teacher. 

Whenever practicable, the label should be written directly on the object. Other- 
wise, it should be written on paper (6 by 10 mm.), and this pasted on the object. In 
ie cases both methods are impracticable; then the various objects should be kept 
ay, but the card will refer to these objects as if they were numbered. 

49G. We transcribe, as examples, the cards which are used by us for articles 28 
and 190. 

•The black-board work is carried to an extreme in most of our schools. The use 
of dry rubbers is very objectionable— gives too much chalk dust in the room. Damp 
sponges should be used instead. 



Elements of Physics. 161 



J? da. r^ieeefec aiaveYu e/ me/a/d. 



] oeetanaa/al fitccftd #■/: 



zna& 

f, /eaa; J2, Uon; <3, Yen; ^, dieted; d, duvet. 
#, $, eenfaneJei tate. 



'fee eziat/etu c/ vtteYezena dJoned 



veeJanaa/eet v/eend of: 
f, wAeee maivte; J2, ateiu uined/ene; <3, tea daneufone; /?, 
toeuoui dantzdJone. 

<J&uc, S, a een&'tnecei teue. 



^oe. fi^iecefec atavefu o/ tetooez, e&. 

oec/anaeiiai v/cend o/; 
/, oem; J2, v/aen <wa/n€iJ; S, cAeiiM; *£, fane; S, ecin; V, 



aeadd. 



do, /, a eenametet ia/e. 



In the first case, it is not convenient to write the label on the object. In the othfcr 
two cases the label is written on the specimen. Thus : The red sandstone has thO 
label 28b/3. The cork has the label 28c/5, etc. 

/f^. viMd-fail e/ \£u'eem. 

— - aicnvn tit nuaa/e c/ dwedeon. x^fea. J/. 

Javeuai eludfa/, z&bmeez <m uo&om e/ veddet. %trea. Jo. 

*|? /aye c^dta/. S4. Jf. 

21 



190 

1 

190 
2 



162 Guide to the Study of the 



The label (i. e. the double number), is written on a small strip of paper, through 
which the pin pusses, which carries the corresponding crystal. Of course, more 
than three crystals may be given in this article. 

Much more should be said about this and many kindred subjects. The author 
has started a journal, called The School Laboratory, especially devoted to the prac- 
tical instruction in physical science, to which, both student and teacher, are refer- 
red for further details. All matters of interest, both to student and teacher, will be 
collected in a simple and practical form in that journal, which also will give full in- 
formation as to the best mode of preparing and purchasing apparatus. 

497. The student should never commence reduction, that is, the calculation of his 
experiments, until the entire series is completed. Only in this manner can the de- 
terminations be quite unbiased. 

If but a limited time can be devoted to this study, these reductions should all be 
made at home.* Guard against errors in calculations— repeat the calculations now 
and then. 

In this connection we advise the teacher to see that the students write plain fig- 
ures, destitute of any ornament, flourish, or circumvolutions. The figures should, 
moreover, be all of the same size, uniform in position. The elegance of simplicity 
resulting cannot be too highly recommended. The same remarks apply, with al- 
most equal force, to the writing in the journal. 

Wherever several determinations of the same quality are made, the mean of these 
several determinations should always be calculated and given. 

I find it constantly necessary to remind students of what is said about concrete 
and abstract numbers in 22. The digit zero is of as much importance as 3, 5, or any 
other, and, therefore, should be put down. If you find a weight 1, and not one-tenth 
less nor more, then it is 1.0 and the zero must be written, for it has been determined. 
In the same manner in 0.1, the zero should be written, and not merely .1 as they do> 
it seems, in certain young ladies' seminaries. Again, do not add a zero or any other 
digit, unless you have determined it; thus, if you found 1.1 and have not proved 
that the hundredth is nought, do not write 1.10. 

The teacher will have to watch the students closely on this subject. 

498. The teacher should give his personal attention to each student— make reg- 
ular minds, passing from one to the other. He should carefully notice everything 
the student does — commend what deserves commendation, and carefully correct er- 
rors in handling of apparatus, in writing, in calculation, etc. Only if the teacher is 
thoroughly at home in the work, will he be able to do as required, and instruct with 
profit. It will be seen, how different this mode of instruction is from the popular 
" hearing a recitation." 

The teacher should most carefully avoid giving the student any information direct, 
which the student can obtain from his manual, or irom the objects before him. If 
the student, in question, fails to obtain it, the teacher should, in the presence of the 
former, call upon a neighbor student. Our students learn, as a rule, so much abou^. 
words in regard to spelling, form, gender, case, inflexion, conjugation, declension 
etc., etc., that they are very liable to entirely loose sight of the fact, that words also 
are u^-ed to convey some meaning. Hence, the teacher will find it frequently neces- 
sary lo point to the particular spot in the book where a manipulation or an operation 
is described, when he sees a student doing it incorrectly. Suppose he notices that 
a student reads of the upper level of a liquidln a graduated cylinder — then the teach- 
er should refer the student to the second paragraph of 11. If a student removes the 
ghts from the scale pan and thus from memory puts down the weight in his book 
— the teacher should have him turn to 18, immediately. So in all cases. Only in 
this ' acquire the great art of reading with understanding . Our 

voluminous text-books, some four to eight hundred pages per term, exert a very 
destructive influence on the intellect of the young. 

*Of cour-e, only the result of the calculations is entered in the journal, not the 
actual multiplication, etc. All such figuring is done on loose slips of paper. 



Elements of Physics. 163 



499. While thus watching and superintending the young experimenters at 
work, the teacher should also question each one, separately, on the subject which 
he is studying. Questions on the apparatus used, the mode of experimentation em- 
ployed, the conclusion derived, the degree of accuracy and certainty established, the 
causes of error, the application of the principle or apparatus in life— all should re- 
ceive the attention which the case demands. 

In this way sound habits of study and reasoning are inculcated in the young ; they 
are no longer mere members of a class, but they are individual students, each one 
equally, reading, thinking, experimenting, and observing, carefully guided by the 
hand and word of the teacher. 

500* As repeatedly remarked, the teacher may now and then explain some ex- 
tra apparatus which he may possess— may, in fact, develop some points of the sub- 
ject more in detail. Still such work should only be attempted with great judgment 
and after great care and preparation on the part of the teacher. 

The student may also, as he advances, read other works on physics, which in com- 
parison to the present may properly be regarded as simple reading-books on this 
subject. 

However, we cannot too strongly urge both teacher and student, to first thor- 
oughly master these elements. Thereby, a solid foundation will have been laid for 
further study and reflection. 

This book will never be popular; it requires too much for that, both of teacher and 
student. But a few of those teachers, who are thoroughly in earnest, and who are 
determined to inculcate the true spirit of cautious, patient, and thorough investiga- 
tion, will also possess that degree of self-denial which the faithful use of these " Ele- 
ments of Physics " requires on the part of the teacher ; and such teachers will, we 
know from experience, be richly rewarded by the progress in thorough knowledge 
which many of the students will make, as with their own young hands they dip the 
water of truth from the pure fountain of nature. 



PKOBLEMS.* 



1. How many dollars was the Australian "Barkley Nugget" worth, which weighed 
146 pounds avoirdupois, supposing the mass to have been pure gold, except only the 
6 ounces of gangue? How many cubic centimeters of gold in this nugget? 

2. Find the weight in kilogrammes of one million dollars of fine gold. Find 
its volume in cubic centimeters and in cubic inches. 

3. How many dollars is the value of one cubic centimeter of fine gold? How 
much the same volume of fine silver, if the specific gravity of fine silver is 10.5 ? 

4:. The walls of a building are 30 meters high, 1.21 meters thiok, and consist of 
sand-stone of specific gravity 2.5. How great will be the pressure on the foundation 
per running meter of this wall? How much per square centimeter? 

5« From a granite boulder (sp. grav. 2.65) has been cut a rectangular prism, the 
sides of the base being 0.5 meters, while the height is 5 meters. How great is its 
weight ? 

6. How many horses will be required to move the granite prism (problem 5) on 
a sandy road, on a proper wagon (see 102 and 84)? and how far will these horses 
be able to move the same in three hours ? 

7. A young man intends to visit a friend, who lives in a town ten miles distant. 
A river covered with very smooth ice would permit him to make the trip, on flat steel 
skates, in one hour and a half; but his friends think that he is not able to stand 
this exertion. He insists that he can do so, because he has, during as long a time, 
by means of a light shovel, thrown 100 liters of water 1 meter high per minute. 
Calculate the mechanical work to be performed in each case, in order thereby to 
decide this dispute, supposing the internal work to be about the same in both 
cases. 

8. How many liters of water (acting on any turbine) under a head (or fall) of 
ten meters, are equivalent to the combustion of one kilogramme of coal (burnt un- 
der the boiler of a steam engine)? 

9. How many horse-powers can be obtained by a brook yielding 16 liters per 
second, and having a fall of 1.31 meters ? 

10. From a coal mine 100 meters deep, 100,000 kilogrammes of water per hour 
are to be removed by means of a pump, the coefficient of useful effect of which is 
0.60. How much coal will have to be consumed per hour under a common steam 
engine, yielding 0.1 of the total mechanical work of the burning coal ? [See 486.] 

11. How many men would be required to do this work, if fourteen men are able 
to replace one horse-power, and can work eight hours out of the twenty-four ? 

12. A stamp mill connected with a blast furnace, at Hayange, France, contained 
thirty-two stamp*, each weighing 80.1 kilogrammes, and each lifted 50 times per 
minute 0.818 meters high, was moved by 9.53 horse-power. What is the coefficient 
of useful effect of this machine? How much coal will be burnt per hour under the 
boiler of the steam engine (effect 0.1) supplying the force? How much water per 
minute, having I fail of 5 meters, would be required to yield the same power, if the 
coefficient of the turbine used is 0.7 ? How many men, working eight hours out of 
twenty-four, wouM he required to keep the stamp mill constantly at work ? 



♦Problems 1 to 12 require only calculations; from 13 onward, nearly all require 
Constructions be-' 



Problems. 165 



13. A block of wood, weighing 100 kilogrammes, slides down an inclined plane 
of wood, 100 meters long and 10 meters high. How great a mechanical work will 
this block exert by striking a body at the foot of the plane ? How great is the co- 
efficient of useful effect of this machine ? How will these answers be, if the block 
and the inclined plane are lubricated with tallow ? 

14. How great a power is required to move a wooden sleigh up a wooden plank 
inclined 32 degrees to the horizon, if sleigh and load weigh 500 kilogrammes, and 
if the power acts parallel to the plank — the coefficient of friction 0.4? How great a 
mechanical work will be performed by moving this sleigh 100 meters on this plank ? 
Considered as a machine, what is the coefficient of useful effect ? 

15. On a point are applied the forces 20, 35, and 70 kilogrammes acting in one 
direction, and the forces 10, 45, 15, and 30 acting in the opposite direction on the 
same line. By means of how great an additional force will equilibrium be pro- 
duced ? 

16. The forces P=3 kilogrammes and Q=4 kilogrammes act under a right angle 
on the same point. Find the resultant R and the angles formed by R with the 
components. 

17. The forces P=Q=100 act on the same point A, under an angle of 45 degrees. 
Find the resultant in magnitude and direction. 

18. The forces P=100 and Q=50 include an angle of 145 degrees. Find the re- 
sultant in magnitude and direction. 

19. Nine equal forces act on the same point in directions which form the fol- 
lowing angles with a fixed direction; viz: 0, 30, 45, 60, 90, 120, 135, 150, and 180 
degrees. Find the resultant in magnitude and direction. Best solved by decom- 
posing each force in two components, one in the fixed direction (X), and the other 
(5T) at right angles thereto. 

20. The force R=100 is to be decomposed into two forces forming the angles 
PR=65 and QR=25 degrees with R. Find the components P and Q. 

21. The force R=100 is to be replaced by two forces, P=200 and Q=300. Find 
the directions in which these new forces must act. 

22. A perpendicular staff, 2.5 meters high, throws a shadow 1.63 meters long, on 
a level ground. Find the altitude of the sun. 

23. How long the rafters, and how high the roof, inclined 35 degrees to the hori- 
zon, if the walls are 12 meters apart ? 

24. The sides of a rectangle are b and h, according to measurement ; the pos- 
sible error in each is e. How great is the possible error of the area a of the rect- 
angle? Example, e=0.1 millimeter and h=200 b=100 centimeters. 

25. The three edges of a rectangular block are measured h, 1, b, each with a 
possible error of e. How great the possible error of the volume resulting? Exam- 
ple, e=0.1 millimeter, and h=200, b=l=400 centimeters. 



166 



Factors. 



FACTORS, 

FOR THE REDUCTION OF ENGLISH TO METRIC UNITS, AND OF METRIC 
TO ENGLISH UNITS. 



LISH TO METRIC. I. LENGTHS. 

1 inch 25.40 ram. 

1 foot 304.S0 mm. 

1 mile 1609.2-1 m. 



METRIC TO ENGLISH. 

1 meter 39,370 inches. 

1 kilometer 3280.84 feet. 

0.6214 miles. 



ENGLISH TO METRIC. II. AREAS 

1 square inch 6.452 square cm. 

1 square foot 9.2904 square dm 

1 acre 0.4047 hectare. 

1 square mile 259.0 hectare. 



METRIC TO ENGLISH. 

1 square meter 1550 square inches. 

" 10.764 square feet. 

1 hectare* 2.4710 acres. 

1 sq. kilometer 0.38610 square miles 



ENGLISH TO METRIC. III. VOLUMES. METRIC TO ENGLISH. 

1 litre 61.024 cubic inches. 

1 steref 35.314 cubic feet. 

" 1.3079 cubic yards. 

1 hectolitre 2.8379 bushels. 

" 26.4170 wine gallons. 

" 105.68 wine quarts. 

1 litre 33.814 fluid ounces. 



1 cubic inch 16.388 cc. 

1 cubic foot 28.318 litres. 

1 cubic yard 764.57 litres. 

1 bushel 35.240 litres. 

1 wine gallon 3.7854 litres. 

1 wine quart 946.36 cc. 

1 fluid ounce 29.574 cc. 



ENGLI8H TO METRIC. 



IV. WEIGHTS. 



1 grain 0.064S0 gr. 

1 troy ounce 31.1038 gr. 

1 avoirdupois ounce 28.350 gr. 

1 pound 453.60 gr. 

1 short ton [2000 ft>s] 907.20 kgr. 

1 long ton [2240 fibs] 1016.06 kgr. 



METRIC TO ENGLISH. 



1 gramme 15.4322 grains. 

1 kilogramme 32.1504 troy oz. 

" 35.274 avoirdupois oz, 

" 2.20460 " as. 

1 tonneairt 1.10230 short tons. 



..0.98420 long tons. 



ENGLISH TO METRIC. V. DYNAMOS. 

1 pound foot 0.1383 kgr M. | 1 kgr M.. 



METRIC TO ENGLISH. 

7.2331 pound feet. 



* One hectare is 100 ares, each are 10 meters square, or 100 square meters ; hence 
a hectare is 10,000 square meters 

fStere — 1 cubic meter. 

X Tonneau — millier — 1000 kgr. 



Table for Reduction. 



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JOURNAL OF EXPERIMENTS 



IN 



HINEICHS' 



ELEMENTS OF PHYSICS, 



PERFORMED IX TIIE 



\ 



SCHOOL LABORATORY, 



UNDER THE DIRECTION OF 



BY 






AT 






LABORATORY EULES. 



1. Be Quiet. — Talk not to your fellow students, and only in low 
whisper to your teacher. Walk to and from the balance so that your 
steps are not heard. Early learn thus to show reverence for truth and 
its investigation ; the labaratory should be a temple of science. 

2. Be Careful.— Handle every apparatus precisely as directed, 
and as if it would require a fortune to replace it. See that everything 
is in good order when you receive it, and take an honest pride in re- 
turning it in excellent order to your teacher. If you injure an}^thing, 
frankly take it to your teacher, and pay enough to repair the injury 
and the loss. 

3. Be Certain. — Do everything so that no doubt can arise. Meas- 
ure, w T eigh, and record as directed, then you will be sure. Do no^ 
trust to your memory. Do not assert anything of which you are not 
sure. Never guess — at most, estimate. 



HOW TO KEEP THE JOURNAL. 



Page this journal as a continuation of the book. At the upper right 
hand enter the date, upper left hand, the article of the book to be de- 
monstrated by your experiment. As heading of page write concisely and 
plainly the subject investigated. On the proper place, in the margin 
of the text, enter the number of the page of the journal where these 
experiments are recorded. In this manner you can readily turn from 
the text to the experiments, and from the experiments to the text. 
Never omit to do this. The author only directs your work, you dis- 
cover the truth of the laws for yourself. 

Keep your journal perfectly clean, and nice, write plainly and ele- 
gantly ; do not crowd words and figures together, but leave ample room 
in margin. For specimens, see following page. 



1 of Ej nts. 173 



30 



<-/ uiuaj; t>c/a//e tin wa&i 








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, 



^£&ni& (/ accuracy / /;/ *') 



Author's Xoticz. — This page is to show nor only the results obtained, bid also the 
precise method of record used. Ample space should always be taken — no crowding 
ol figures or words. 

On the following pages we gire only the results in form, but crowd thei 
as much as type admits of. 

We add the name and place of residence of our students from whose Joni 
the series here printed hate been taken. Of course only go&.i work has been se- 
lected: Dut wehaYe an abundance of material equally good in the Jour::;/.. ■:: thes . 
and other students of our c] 



171 



Elements of Physics. 



41 a 






48 



b. 



Jfo. 


I 


to 


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to y 


e 


1 


10.0 


3.7 


0.36 


3.70 


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2 


8.0 


8.0 


0.36 


2.96 


0.04 


SI 


4.0 


1.5 


0.37 


1.48 


0.02 


4 


2.6 


1.0 


0.38 


0.96 


0.04 


5 


1.0 


0.4 


0.40 


0.37 


0.03 



c = 0.37 

i. <y&€in (Pomona, t^o* 



?tY,/. 



amiaiy /J2. / 



tjJlea <?* v?itci€. 



Models used. — Four circles of different radii, 
cut from homogeneous zinc sheet ; also a rectan= 
gle (from the same), of exactly 2 by 5 cm. 

r is a mean of four different measurements ; 
c is zv eight of 1 sq. cm. of plate used; c=o.^jS. 



1 


Jsfo. 1. 


JVo. 2. 


JJo. 3. 


JVo. 4 


r 1 


2.71 


3.25 


3.55 


4.35 


* 2 


7.34 


10.56 


12.60 


; 18.92 


to 


7.79 


11.20 


13.45 


20.24 


a 


23.03 


33.16 


39.79 


59.59 




8.510 


| 10.203 


11.208 


13.698 


(r* 


3.141 


3.140 


3.150 


3.141 


ror 


0.003 


0.001 


0.009 


0.000 



^At/u ^yftaiv iJvyan, 



Csvode iffie//. 



MAR 241950 



Journal of Experiments. 



175 



i 



1 
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17G 



Elements of Physics. 



94> 



January 31, iSji. 
The Lever. Series I. 



67.1. 



(R = 80.8. 



<R 



= 0.8303. 



Momenta. 



JVo. 


r 


P' 


r 


d 


(?P' 


for* 


1 


12.0 


14.45 


0.8305 


0.0002 


869.6 


869.6 


2 


13.0 


15.65 


0.8308 


0.0005 


1050.1 


1050.4 


3 


14.0 


16.85 


0.8307 


0.0004 


1131.6 


1131.2 


4 


15.0 


18.05 


0.8310 


0.0007 


1211.9 


1212.0 


5 


16.0 


19.25 


0.8311 


0.0008 


1292.6 


1292.8 


6 


18.0 


21.70 


0.8309 


0.0006 


1455.1 


1454.4 



Miss Mora Sale, Iowa City. 

101. January lg, 1871. 

Sliding Friction. 

Series II. Cherry Wood on Maple Wood. 
Grain, parallel; size of cherry, 10 by 10 cm. 



JVo. 


at 


<p 


f=l 


* 


410 


120 


0.292 


2 


540 


145 


0.268 




| 620 


165 


0.266 


4 


705 


ISO 


0.255 


5 


820 


210 


0.256 


6 


920 


230 


0.250 


7 


980 


245 


0.250 


8 


| 1100 


275 


0.250 



Mean of 4 to 8 ; c=o.2ji. JIos. 1 to 3 show 
ct of adhesion, (R being small. 

Mr. Henry Z. (Burkart, Marshalltown. 



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